diff --git a/doc/pub/week39/html/week39-bs.html b/doc/pub/week39/html/week39-bs.html
index 899adc049..27c968c67 100644
--- a/doc/pub/week39/html/week39-bs.html
+++ b/doc/pub/week39/html/week39-bs.html
@@ -147,6 +147,10 @@ doconce format html week39.do.txt --html_style=bootstrap --pygments_html_style=d
                2,
                None,
                'gradient-descent-and-ridge'),
+              ('The Hessian matrix for Ridge Regression',
+               2,
+               None,
+               'the-hessian-matrix-for-ridge-regression'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
@@ -292,36 +296,37 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._week39-bs042.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
      <!-- navigation toc: --> <li><a href="._week39-bs043.html#and-a-corresponding-example-using-scikit-learn" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
      <!-- navigation toc: --> <li><a href="._week39-bs044.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs045.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs046.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs047.html#challenge-yourself" style="font-size: 80%;">Challenge yourself</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs048.html#friday-october-1" style="font-size: 80%;">Friday October  1</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs049.html#stochastic-gradient-descent" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs050.html#computation-of-gradients" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs051.html#sgd-example" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs052.html#the-gradient-step" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs053.html#simple-example-code" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs054.html#when-do-we-stop" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs055.html#slightly-different-approach" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs056.html#program-for-stochastic-gradient" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs057.html#momentum-based-gd" style="font-size: 80%;">Momentum based GD</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs058.html#more-on-momentum-based-approaches" style="font-size: 80%;">More on momentum based approaches</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs059.html#momentum-parameter" style="font-size: 80%;">Momentum parameter</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs060.html#second-moment-of-the-gradient" style="font-size: 80%;">Second moment of the gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs061.html#rms-prop" style="font-size: 80%;">RMS prop</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs062.html#adam-optimizer" style="font-size: 80%;">ADAM optimizer</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs063.html#practical-tips" style="font-size: 80%;">Practical tips</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs064.html#automatic-differentiation" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs065.html#using-autograd" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs066.html#autograd-with-more-complicated-functions" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs067.html#more-complicated-functions-using-the-elements-of-their-arguments-directly" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs068.html#functions-using-mathematical-functions-from-numpy" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs069.html#more-autograd" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs070.html#and-with-loops" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs071.html#using-recursion" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs072.html#unsupported-functions" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs073.html#the-syntax-a-dot-b-when-finding-the-dot-product" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._week39-bs074.html#recommended-to-avoid" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs045.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs046.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs047.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs048.html#challenge-yourself" style="font-size: 80%;">Challenge yourself</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs049.html#friday-october-1" style="font-size: 80%;">Friday October  1</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs050.html#stochastic-gradient-descent" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs051.html#computation-of-gradients" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs052.html#sgd-example" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs053.html#the-gradient-step" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs054.html#simple-example-code" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs055.html#when-do-we-stop" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs056.html#slightly-different-approach" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs057.html#program-for-stochastic-gradient" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs058.html#momentum-based-gd" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs059.html#more-on-momentum-based-approaches" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs060.html#momentum-parameter" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs061.html#second-moment-of-the-gradient" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs062.html#rms-prop" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs063.html#adam-optimizer" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs064.html#practical-tips" style="font-size: 80%;">Practical tips</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs065.html#automatic-differentiation" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs066.html#using-autograd" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs067.html#autograd-with-more-complicated-functions" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs068.html#more-complicated-functions-using-the-elements-of-their-arguments-directly" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs069.html#functions-using-mathematical-functions-from-numpy" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs070.html#more-autograd" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs071.html#and-with-loops" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs072.html#using-recursion" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs073.html#unsupported-functions" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs074.html#the-syntax-a-dot-b-when-finding-the-dot-product" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._week39-bs075.html#recommended-to-avoid" style="font-size: 80%;">Recommended to avoid</a></li>
 
         </ul>
       </li>
@@ -351,7 +356,7 @@ MathJax.Hub.Config({
 </center>
 <br>
 <center>
-<h4>Nov 2, 2021</h4>
+<h4>Nov 3, 2021</h4>
 </center> <!-- date -->
 <br>
 
@@ -376,7 +381,7 @@ MathJax.Hub.Config({
   <li><a href="._week39-bs008.html">9</a></li>
   <li><a href="._week39-bs009.html">10</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._week39-bs074.html">75</a></li>
+  <li><a href="._week39-bs075.html">76</a></li>
   <li><a href="._week39-bs001.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/week39/html/week39-reveal.html b/doc/pub/week39/html/week39-reveal.html
index bd6faa596..de1877466 100644
--- a/doc/pub/week39/html/week39-reveal.html
+++ b/doc/pub/week39/html/week39-reveal.html
@@ -184,7 +184,7 @@ MathJax.Hub.Config({
 </center>
 <br>
 <center>
-<h4>Nov 2, 2021</h4>
+<h4>Nov 3, 2021</h4>
 </center> <!-- date -->
 <br>
 
@@ -1760,6 +1760,26 @@ $$
 <p>&nbsp;<br>
 </section>
 
+<section>
+<h2 id="the-hessian-matrix-for-ridge-regression">The Hessian matrix for Ridge Regression </h2>
+<p>The Hessian matrix of Ridge Regression for our simple example  is given by </p>
+<p>&nbsp;<br>
+$$
+\boldsymbol{H} \equiv \begin{bmatrix}
+\frac{\partial^2 C(\beta)}{\partial \beta_0^2} & \frac{\partial^2 C(\beta)}{\partial \beta_0 \partial \beta_1}  \\
+\frac{\partial^2 C(\beta)}{\partial \beta_0 \partial \beta_1} & \frac{\partial^2 C(\beta)}{\partial \beta_1^2} &  \\
+\end{bmatrix} = \frac{2}{n}X^T X+2\lambda\boldsymbol{I}.
+$$
+<p>&nbsp;<br>
+
+<p>This implies that the Hessian matrix  is positive definite, hence the stationary point is a
+minimum.
+Note that the Ridge loss function is convex, as a sum of two convex
+functions. Therefore, the stationary point is a global
+minimum of this function.
+</p>
+</section>
+
 <section>
 <h2 id="program-example-for-gradient-descent-with-ridge-regression">Program example for gradient descent with Ridge Regression </h2>
 
@@ -1787,14 +1807,21 @@ XT_X = X.T @ X
 
 <span style="color: #228B22">#Ridge parameter lambda</span>
 lmbda  = <span style="color: #B452CD">0.001</span>
-Id = lmbda* np.eye(XT_X.shape[<span style="color: #B452CD">0</span>])
+Id = n*lmbda* np.eye(XT_X.shape[<span style="color: #B452CD">0</span>])
+
+<span style="color: #228B22"># Hessian matrix</span>
+H = (<span style="color: #B452CD">2.0</span>/n)* XT_X+<span style="color: #B452CD">2</span>*lmbda
+<span style="color: #228B22"># Get the eigenvalues</span>
+EigValues, EigVectors = np.linalg.eig(H)
+<span style="color: #658b00">print</span>(<span style="color: #CD5555">f&quot;Eigenvalues of Hessian Matrix:{</span>EigValues<span style="color: #CD5555">}&quot;</span>)
+
 
 beta_linreg = np.linalg.inv(XT_X+Id) @ X.T @ y
 <span style="color: #658b00">print</span>(beta_linreg)
 <span style="color: #228B22"># Start plain gradient descent</span>
 beta = np.random.randn(<span style="color: #B452CD">2</span>,<span style="color: #B452CD">1</span>)
 
-eta = <span style="color: #B452CD">0.1</span>
+eta = <span style="color: #B452CD">1.0</span>/np.max(EigValues)
 Niterations = <span style="color: #B452CD">100</span>
 
 <span style="color: #8B008B; font-weight: bold">for</span> <span style="color: #658b00">iter</span> <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(Niterations):
diff --git a/doc/pub/week39/html/week39-solarized.html b/doc/pub/week39/html/week39-solarized.html
index add781ae1..5bdeff9da 100644
--- a/doc/pub/week39/html/week39-solarized.html
+++ b/doc/pub/week39/html/week39-solarized.html
@@ -174,6 +174,10 @@ div.toc p,a {
                2,
                None,
                'gradient-descent-and-ridge'),
+              ('The Hessian matrix for Ridge Regression',
+               2,
+               None,
+               'the-hessian-matrix-for-ridge-regression'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
@@ -278,7 +282,7 @@ MathJax.Hub.Config({
 </center>
 <br>
 <center>
-<h4>Nov 2, 2021</h4>
+<h4>Nov 3, 2021</h4>
 </center> <!-- date -->
 <br>
 
@@ -1701,6 +1705,23 @@ $$
 $$
 
 
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+<h2 id="the-hessian-matrix-for-ridge-regression">The Hessian matrix for Ridge Regression </h2>
+<p>The Hessian matrix of Ridge Regression for our simple example  is given by </p>
+$$
+\boldsymbol{H} \equiv \begin{bmatrix}
+\frac{\partial^2 C(\beta)}{\partial \beta_0^2} & \frac{\partial^2 C(\beta)}{\partial \beta_0 \partial \beta_1}  \\
+\frac{\partial^2 C(\beta)}{\partial \beta_0 \partial \beta_1} & \frac{\partial^2 C(\beta)}{\partial \beta_1^2} &  \\
+\end{bmatrix} = \frac{2}{n}X^T X+2\lambda\boldsymbol{I}.
+$$
+
+<p>This implies that the Hessian matrix  is positive definite, hence the stationary point is a
+minimum.
+Note that the Ridge loss function is convex, as a sum of two convex
+functions. Therefore, the stationary point is a global
+minimum of this function.
+</p>
+
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="program-example-for-gradient-descent-with-ridge-regression">Program example for gradient descent with Ridge Regression </h2>
 
@@ -1728,14 +1749,21 @@ XT_X = X.T @ X
 
 <span style="color: #228B22">#Ridge parameter lambda</span>
 lmbda  = <span style="color: #B452CD">0.001</span>
-Id = lmbda* np.eye(XT_X.shape[<span style="color: #B452CD">0</span>])
+Id = n*lmbda* np.eye(XT_X.shape[<span style="color: #B452CD">0</span>])
+
+<span style="color: #228B22"># Hessian matrix</span>
+H = (<span style="color: #B452CD">2.0</span>/n)* XT_X+<span style="color: #B452CD">2</span>*lmbda
+<span style="color: #228B22"># Get the eigenvalues</span>
+EigValues, EigVectors = np.linalg.eig(H)
+<span style="color: #658b00">print</span>(<span style="color: #CD5555">f&quot;Eigenvalues of Hessian Matrix:{</span>EigValues<span style="color: #CD5555">}&quot;</span>)
+
 
 beta_linreg = np.linalg.inv(XT_X+Id) @ X.T @ y
 <span style="color: #658b00">print</span>(beta_linreg)
 <span style="color: #228B22"># Start plain gradient descent</span>
 beta = np.random.randn(<span style="color: #B452CD">2</span>,<span style="color: #B452CD">1</span>)
 
-eta = <span style="color: #B452CD">0.1</span>
+eta = <span style="color: #B452CD">1.0</span>/np.max(EigValues)
 Niterations = <span style="color: #B452CD">100</span>
 
 <span style="color: #8B008B; font-weight: bold">for</span> <span style="color: #658b00">iter</span> <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(Niterations):
diff --git a/doc/pub/week39/html/week39.html b/doc/pub/week39/html/week39.html
index 5c0ddf7a9..43c6269bc 100644
--- a/doc/pub/week39/html/week39.html
+++ b/doc/pub/week39/html/week39.html
@@ -251,6 +251,10 @@ div.toc p,a {
                2,
                None,
                'gradient-descent-and-ridge'),
+              ('The Hessian matrix for Ridge Regression',
+               2,
+               None,
+               'the-hessian-matrix-for-ridge-regression'),
               ('Program example for gradient descent with Ridge Regression',
                2,
                None,
@@ -355,7 +359,7 @@ MathJax.Hub.Config({
 </center>
 <br>
 <center>
-<h4>Nov 2, 2021</h4>
+<h4>Nov 3, 2021</h4>
 </center> <!-- date -->
 <br>
 
@@ -1778,6 +1782,23 @@ $$
 $$
 
 
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+<h2 id="the-hessian-matrix-for-ridge-regression">The Hessian matrix for Ridge Regression </h2>
+<p>The Hessian matrix of Ridge Regression for our simple example  is given by </p>
+$$
+\boldsymbol{H} \equiv \begin{bmatrix}
+\frac{\partial^2 C(\beta)}{\partial \beta_0^2} & \frac{\partial^2 C(\beta)}{\partial \beta_0 \partial \beta_1}  \\
+\frac{\partial^2 C(\beta)}{\partial \beta_0 \partial \beta_1} & \frac{\partial^2 C(\beta)}{\partial \beta_1^2} &  \\
+\end{bmatrix} = \frac{2}{n}X^T X+2\lambda\boldsymbol{I}.
+$$
+
+<p>This implies that the Hessian matrix  is positive definite, hence the stationary point is a
+minimum.
+Note that the Ridge loss function is convex, as a sum of two convex
+functions. Therefore, the stationary point is a global
+minimum of this function.
+</p>
+
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="program-example-for-gradient-descent-with-ridge-regression">Program example for gradient descent with Ridge Regression </h2>
 
@@ -1805,14 +1826,21 @@ XT_X <span style="color: #666666">=</span> X<span style="color: #666666">.</span
 
 <span style="color: #408080; font-style: italic">#Ridge parameter lambda</span>
 lmbda  <span style="color: #666666">=</span> <span style="color: #666666">0.001</span>
-Id <span style="color: #666666">=</span> lmbda<span style="color: #666666">*</span> np<span style="color: #666666">.</span>eye(XT_X<span style="color: #666666">.</span>shape[<span style="color: #666666">0</span>])
+Id <span style="color: #666666">=</span> n<span style="color: #666666">*</span>lmbda<span style="color: #666666">*</span> np<span style="color: #666666">.</span>eye(XT_X<span style="color: #666666">.</span>shape[<span style="color: #666666">0</span>])
+
+<span style="color: #408080; font-style: italic"># Hessian matrix</span>
+H <span style="color: #666666">=</span> (<span style="color: #666666">2.0/</span>n)<span style="color: #666666">*</span> XT_X<span style="color: #666666">+2*</span>lmbda
+<span style="color: #408080; font-style: italic"># Get the eigenvalues</span>
+EigValues, EigVectors <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>eig(H)
+<span style="color: #008000">print</span>(<span style="color: #BA2121">f&quot;Eigenvalues of Hessian Matrix:</span><span style="color: #BB6688; font-weight: bold">{</span>EigValues<span style="color: #BB6688; font-weight: bold">}</span><span style="color: #BA2121">&quot;</span>)
+
 
 beta_linreg <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(XT_X<span style="color: #666666">+</span>Id) <span style="color: #666666">@</span> X<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y
 <span style="color: #008000">print</span>(beta_linreg)
 <span style="color: #408080; font-style: italic"># Start plain gradient descent</span>
 beta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(<span style="color: #666666">2</span>,<span style="color: #666666">1</span>)
 
-eta <span style="color: #666666">=</span> <span style="color: #666666">0.1</span>
+eta <span style="color: #666666">=</span> <span style="color: #666666">1.0/</span>np<span style="color: #666666">.</span>max(EigValues)
 Niterations <span style="color: #666666">=</span> <span style="color: #666666">100</span>
 
 <span style="color: #008000; font-weight: bold">for</span> <span style="color: #008000">iter</span> <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(Niterations):
diff --git a/doc/pub/week39/ipynb/ipynb-week39-src.tar.gz b/doc/pub/week39/ipynb/ipynb-week39-src.tar.gz
index 0b3705d4b..696a61d56 100644
Binary files a/doc/pub/week39/ipynb/ipynb-week39-src.tar.gz and b/doc/pub/week39/ipynb/ipynb-week39-src.tar.gz differ
diff --git a/doc/pub/week39/ipynb/week39.ipynb b/doc/pub/week39/ipynb/week39.ipynb
index d28a86b34..2dcb4789c 100644
--- a/doc/pub/week39/ipynb/week39.ipynb
+++ b/doc/pub/week39/ipynb/week39.ipynb
@@ -2,7 +2,7 @@
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     "# Week 39: Optimization and  Gradient Methods\n",
     "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
     "\n",
-    "Date: **Nov 2, 2021**\n",
+    "Date: **Nov 3, 2021**\n",
     "\n",
     "Copyright 1999-2021, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license"
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-   "id": "2367ba74",
+   "id": "bd42e48a",
    "metadata": {
     "editable": true
    },
@@ -1534,7 +1534,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "20788d85",
+   "id": "6f4210b4",
    "metadata": {
     "editable": true
    },
@@ -1546,7 +1546,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ea535aea",
+   "id": "74bb3e7d",
    "metadata": {
     "editable": true
    },
@@ -1557,7 +1557,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "165adcbc",
+   "id": "beb6c7cc",
    "metadata": {
     "editable": true
    },
@@ -1569,7 +1569,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f7aaa007",
+   "id": "4fd3b390",
    "metadata": {
     "editable": true
    },
@@ -1580,7 +1580,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "23efba9c",
+   "id": "3eb93ca8",
    "metadata": {
     "editable": true
    },
@@ -1591,7 +1591,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d5439727",
+   "id": "79bedfaf",
    "metadata": {
     "editable": true
    },
@@ -1603,7 +1603,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "631c623f",
+   "id": "bd3eca5f",
    "metadata": {
     "editable": true
    },
@@ -1613,7 +1613,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4580be44",
+   "id": "d1cd77fb",
    "metadata": {
     "editable": true
    },
@@ -1625,7 +1625,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3fc0d9f5",
+   "id": "9db15b7e",
    "metadata": {
     "editable": true
    },
@@ -1637,7 +1637,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4b0f7db6",
+   "id": "889d2e82",
    "metadata": {
     "editable": true
    },
@@ -1649,7 +1649,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6062951a",
+   "id": "880fc01f",
    "metadata": {
     "editable": true
    },
@@ -1661,7 +1661,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fd0a2f6e",
+   "id": "19021b89",
    "metadata": {
     "editable": true
    },
@@ -1672,7 +1672,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b83ad4fb",
+   "id": "26f1ca1a",
    "metadata": {
     "editable": true
    },
@@ -1684,7 +1684,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0cd2222f",
+   "id": "b3e4b78f",
    "metadata": {
     "editable": true
    },
@@ -1694,7 +1694,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "de54cca2",
+   "id": "7fb33e80",
    "metadata": {
     "editable": true
    },
@@ -1706,7 +1706,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a090dc8e",
+   "id": "06cbd1cb",
    "metadata": {
     "editable": true
    },
@@ -1716,7 +1716,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4c5bb87a",
+   "id": "15442a6c",
    "metadata": {
     "editable": true
    },
@@ -1728,7 +1728,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e1dc0a5d",
+   "id": "dc60e358",
    "metadata": {
     "editable": true
    },
@@ -1748,7 +1748,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "94780e34",
+   "id": "a4f542bc",
    "metadata": {
     "editable": true
    },
@@ -1760,7 +1760,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7a0f6afb",
+   "id": "85e4bc78",
    "metadata": {
     "editable": true
    },
@@ -1770,7 +1770,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fd14657e",
+   "id": "a0317fc5",
    "metadata": {
     "editable": true
    },
@@ -1782,7 +1782,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ce919c46",
+   "id": "b78c21b7",
    "metadata": {
     "editable": true
    },
@@ -1792,7 +1792,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2af9b699",
+   "id": "428e7a19",
    "metadata": {
     "editable": true
    },
@@ -1803,7 +1803,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "312f6dc3",
+   "id": "0c913ac0",
    "metadata": {
     "editable": true
    },
@@ -1815,7 +1815,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e75a06a8",
+   "id": "57290ae3",
    "metadata": {
     "editable": true
    },
@@ -1827,7 +1827,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "12232187",
+   "id": "67f86200",
    "metadata": {
     "editable": true
    },
@@ -1839,7 +1839,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e44907f2",
+   "id": "008d6c1a",
    "metadata": {
     "editable": true
    },
@@ -1852,7 +1852,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3297c1f5",
+   "id": "24748eec",
    "metadata": {
     "editable": true
    },
@@ -1863,7 +1863,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "abae27bc",
+   "id": "29ebba58",
    "metadata": {
     "editable": true
    },
@@ -1875,7 +1875,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "835b302b",
+   "id": "6f4b4e61",
    "metadata": {
     "editable": true
    },
@@ -1891,7 +1891,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f7a21361",
+   "id": "c9118780",
    "metadata": {
     "editable": true
    },
@@ -1903,7 +1903,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5277ae72",
+   "id": "dffc5b96",
    "metadata": {
     "editable": true
    },
@@ -1914,7 +1914,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cd385e88",
+   "id": "9d1e43aa",
    "metadata": {
     "editable": true
    },
@@ -1926,7 +1926,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "20361729",
+   "id": "d78ff3cf",
    "metadata": {
     "editable": true
    },
@@ -1936,7 +1936,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dd6b22b4",
+   "id": "93268844",
    "metadata": {
     "editable": true
    },
@@ -1948,7 +1948,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "150beb1c",
+   "id": "5ee06e42",
    "metadata": {
     "editable": true
    },
@@ -1958,7 +1958,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "77530681",
+   "id": "c965a705",
    "metadata": {
     "editable": true
    },
@@ -1970,7 +1970,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "04ba2383",
+   "id": "3386391c",
    "metadata": {
     "editable": true
    },
@@ -1980,7 +1980,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ff1a8f53",
+   "id": "4ad90598",
    "metadata": {
     "editable": true
    },
@@ -1992,7 +1992,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f8596b4e",
+   "id": "b0799136",
    "metadata": {
     "editable": true
    },
@@ -2016,7 +2016,7 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "id": "260fdca9",
+   "id": "db78d5b5",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2029,7 +2029,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8884fffe",
+   "id": "a0d1b29e",
    "metadata": {
     "editable": true
    },
@@ -2040,7 +2040,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7269998b",
+   "id": "84e218b8",
    "metadata": {
     "editable": true
    },
@@ -2052,7 +2052,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f8d3cadb",
+   "id": "236e48b7",
    "metadata": {
     "editable": true
    },
@@ -2062,7 +2062,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e9fb7fa",
+   "id": "78b88cb1",
    "metadata": {
     "editable": true
    },
@@ -2074,7 +2074,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d25601f3",
+   "id": "f49f0b6a",
    "metadata": {
     "editable": true
    },
@@ -2088,7 +2088,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3a341c25",
+   "id": "73e5ec0b",
    "metadata": {
     "editable": true
    },
@@ -2104,7 +2104,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aa05f072",
+   "id": "2f1fab67",
    "metadata": {
     "editable": true
    },
@@ -2114,7 +2114,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d9d8e0de",
+   "id": "d05b60d5",
    "metadata": {
     "editable": true
    },
@@ -2126,7 +2126,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d693be2",
+   "id": "44bf44c6",
    "metadata": {
     "editable": true
    },
@@ -2136,7 +2136,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2ea777b4",
+   "id": "f67dfe60",
    "metadata": {
     "editable": true
    },
@@ -2148,7 +2148,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "24834799",
+   "id": "4b5970e0",
    "metadata": {
     "editable": true
    },
@@ -2162,7 +2162,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ca03d184",
+   "id": "9b0183e3",
    "metadata": {
     "editable": true
    },
@@ -2172,7 +2172,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "76b10741",
+   "id": "7d6a7718",
    "metadata": {
     "editable": true
    },
@@ -2183,7 +2183,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "03d8886f",
+   "id": "cefb20c5",
    "metadata": {
     "editable": true
    },
@@ -2198,7 +2198,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "97b0ddb8",
+   "id": "f1769551",
    "metadata": {
     "editable": true
    },
@@ -2208,7 +2208,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "928eefaf",
+   "id": "c590024b",
    "metadata": {
     "editable": true
    },
@@ -2220,7 +2220,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "20ca3352",
+   "id": "f087d2d1",
    "metadata": {
     "editable": true
    },
@@ -2232,7 +2232,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c9e83371",
+   "id": "3f1e8b75",
    "metadata": {
     "editable": true
    },
@@ -2247,7 +2247,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "37af4676",
+   "id": "3257df95",
    "metadata": {
     "editable": true
    },
@@ -2260,7 +2260,7 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "id": "8a3afc9b",
+   "id": "bd5fc754",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2317,7 +2317,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fef51920",
+   "id": "fcea549d",
    "metadata": {
     "editable": true
    },
@@ -2328,7 +2328,7 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "id": "3421b06e",
+   "id": "52a2306c",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2355,7 +2355,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9be51010",
+   "id": "0909287b",
    "metadata": {
     "editable": true
    },
@@ -2367,7 +2367,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f749c999",
+   "id": "d964e991",
    "metadata": {
     "editable": true
    },
@@ -2379,7 +2379,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a3e198f9",
+   "id": "ac0a7e86",
    "metadata": {
     "editable": true
    },
@@ -2389,7 +2389,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d6eb713",
+   "id": "afa5f4fd",
    "metadata": {
     "editable": true
    },
@@ -2403,7 +2403,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "91fab79a",
+   "id": "b7664c73",
    "metadata": {
     "editable": true
    },
@@ -2413,7 +2413,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9107f00b",
+   "id": "6c39dbf3",
    "metadata": {
     "editable": true
    },
@@ -2425,7 +2425,47 @@
   },
   {
    "cell_type": "markdown",
-   "id": "961a44f6",
+   "id": "e67c5e82",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The Hessian matrix for Ridge Regression\n",
+    "The Hessian matrix of Ridge Regression for our simple example  is given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a657b390",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{H} \\equiv \\begin{bmatrix}\n",
+    "\\frac{\\partial^2 C(\\beta)}{\\partial \\beta_0^2} & \\frac{\\partial^2 C(\\beta)}{\\partial \\beta_0 \\partial \\beta_1}  \\\\\n",
+    "\\frac{\\partial^2 C(\\beta)}{\\partial \\beta_0 \\partial \\beta_1} & \\frac{\\partial^2 C(\\beta)}{\\partial \\beta_1^2} &  \\\\\n",
+    "\\end{bmatrix} = \\frac{2}{n}X^T X+2\\lambda\\boldsymbol{I}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8620c333",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "This implies that the Hessian matrix  is positive definite, hence the stationary point is a\n",
+    "minimum.\n",
+    "Note that the Ridge loss function is convex, as a sum of two convex\n",
+    "functions. Therefore, the stationary point is a global\n",
+    "minimum of this function."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "38ce7622",
    "metadata": {
     "editable": true
    },
@@ -2436,7 +2476,7 @@
   {
    "cell_type": "code",
    "execution_count": 12,
-   "id": "b1f705b3",
+   "id": "042531b1",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2461,14 +2501,21 @@
     "\n",
     "#Ridge parameter lambda\n",
     "lmbda  = 0.001\n",
-    "Id = lmbda* np.eye(XT_X.shape[0])\n",
+    "Id = n*lmbda* np.eye(XT_X.shape[0])\n",
+    "\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X+2*lmbda\n",
+    "# Get the eigenvalues\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
     "\n",
     "beta_linreg = np.linalg.inv(XT_X+Id) @ X.T @ y\n",
     "print(beta_linreg)\n",
     "# Start plain gradient descent\n",
     "beta = np.random.randn(2,1)\n",
     "\n",
-    "eta = 0.1\n",
+    "eta = 1.0/np.max(EigValues)\n",
     "Niterations = 100\n",
     "\n",
     "for iter in range(Niterations):\n",
@@ -2490,7 +2537,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b2c5981d",
+   "id": "c7e50920",
    "metadata": {
     "editable": true
    },
@@ -2512,7 +2559,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4c5330ea",
+   "id": "fd1811d9",
    "metadata": {
     "editable": true
    },
@@ -2524,7 +2571,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c15cdad1",
+   "id": "4e9a09ef",
    "metadata": {
     "editable": true
    },
@@ -2534,7 +2581,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fe4260f1",
+   "id": "3aa85e79",
    "metadata": {
     "editable": true
    },
@@ -2551,7 +2598,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6880a7be",
+   "id": "9e269917",
    "metadata": {
     "editable": true
    },
@@ -2564,7 +2611,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da55002d",
+   "id": "e346c2be",
    "metadata": {
     "editable": true
    },
@@ -2577,7 +2624,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "291d4f67",
+   "id": "ed3a06dc",
    "metadata": {
     "editable": true
    },
@@ -2590,7 +2637,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b5587460",
+   "id": "91172463",
    "metadata": {
     "editable": true
    },
@@ -2604,7 +2651,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "347deeb7",
+   "id": "6bf5c088",
    "metadata": {
     "editable": true
    },
@@ -2626,7 +2673,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4ff76de7",
+   "id": "71f4f188",
    "metadata": {
     "editable": true
    },
@@ -2641,7 +2688,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0dabde37",
+   "id": "b0fc4db3",
    "metadata": {
     "editable": true
    },
@@ -2653,7 +2700,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "85053899",
+   "id": "bcd4ddfe",
    "metadata": {
     "editable": true
    },
@@ -2666,7 +2713,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c5d2743e",
+   "id": "3a184799",
    "metadata": {
     "editable": true
    },
@@ -2680,7 +2727,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a3aa78b6",
+   "id": "7fe2c739",
    "metadata": {
     "editable": true
    },
@@ -2691,7 +2738,7 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "id": "3e876868",
+   "id": "90624acc",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2716,7 +2763,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "69f96a04",
+   "id": "844e8019",
    "metadata": {
     "editable": true
    },
@@ -2732,7 +2779,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ab8f6541",
+   "id": "148bcb51",
    "metadata": {
     "editable": true
    },
@@ -2753,7 +2800,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d52641ac",
+   "id": "b4ab6685",
    "metadata": {
     "editable": true
    },
@@ -2776,7 +2823,7 @@
   {
    "cell_type": "code",
    "execution_count": 14,
-   "id": "8168bc67",
+   "id": "69cbdd65",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2811,7 +2858,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2c2826ce",
+   "id": "f30332cd",
    "metadata": {
     "editable": true
    },
@@ -2822,7 +2869,7 @@
   {
    "cell_type": "code",
    "execution_count": 15,
-   "id": "445663c0",
+   "id": "e01570bc",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2897,7 +2944,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aca2efe7",
+   "id": "3282e79d",
    "metadata": {
     "editable": true
    },
@@ -2907,7 +2954,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3f489f9",
+   "id": "4c69c2c8",
    "metadata": {
     "editable": true
    },
@@ -2922,7 +2969,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "36735fa8",
+   "id": "52e6dc92",
    "metadata": {
     "editable": true
    },
@@ -2934,7 +2981,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8e0fd47e",
+   "id": "3c9043ac",
    "metadata": {
     "editable": true
    },
@@ -2952,7 +2999,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "165c45c1",
+   "id": "6ec6074f",
    "metadata": {
     "editable": true
    },
@@ -2971,7 +3018,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "34e9d01d",
+   "id": "409904fd",
    "metadata": {
     "editable": true
    },
@@ -2983,7 +3030,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4fcd3fe2",
+   "id": "7773c363",
    "metadata": {
     "editable": true
    },
@@ -2993,7 +3040,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eef12186",
+   "id": "b138dd03",
    "metadata": {
     "editable": true
    },
@@ -3009,7 +3056,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f1b327ae",
+   "id": "f3a981e7",
    "metadata": {
     "editable": true
    },
@@ -3021,7 +3068,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "843e5f0e",
+   "id": "19d4d326",
    "metadata": {
     "editable": true
    },
@@ -3031,7 +3078,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0b256db8",
+   "id": "6f4ec233",
    "metadata": {
     "editable": true
    },
@@ -3043,7 +3090,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a486e7aa",
+   "id": "80b2287a",
    "metadata": {
     "editable": true
    },
@@ -3053,7 +3100,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bd91d3e0",
+   "id": "f83f8752",
    "metadata": {
     "editable": true
    },
@@ -3065,7 +3112,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fc17ad1e",
+   "id": "4babf4af",
    "metadata": {
     "editable": true
    },
@@ -3081,7 +3128,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f4f69cbf",
+   "id": "162875aa",
    "metadata": {
     "editable": true
    },
@@ -3093,7 +3140,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bedea29a",
+   "id": "42da2213",
    "metadata": {
     "editable": true
    },
@@ -3126,7 +3173,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ff6d5b2c",
+   "id": "76c40c68",
    "metadata": {
     "editable": true
    },
@@ -3138,7 +3185,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7a21b635",
+   "id": "6aa27f9a",
    "metadata": {
     "editable": true
    },
@@ -3156,7 +3203,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "092e7434",
+   "id": "ab85ddc4",
    "metadata": {
     "editable": true
    },
@@ -3166,7 +3213,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ba10fb4a",
+   "id": "6349d4ac",
    "metadata": {
     "editable": true
    },
@@ -3197,7 +3244,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bd7a13b2",
+   "id": "d414cf4b",
    "metadata": {
     "editable": true
    },
@@ -3212,7 +3259,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6ace73dd",
+   "id": "ae053391",
    "metadata": {
     "editable": true
    },
@@ -3230,7 +3277,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "33888962",
+   "id": "8b123165",
    "metadata": {
     "editable": true
    },
@@ -3242,7 +3289,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7665c788",
+   "id": "180086fe",
    "metadata": {
     "editable": true
    },
@@ -3254,7 +3301,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "02b499b9",
+   "id": "950c7627",
    "metadata": {
     "editable": true
    },
@@ -3272,7 +3319,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9ddf4fca",
+   "id": "43e6754e",
    "metadata": {
     "editable": true
    },
@@ -3295,7 +3342,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e5867cac",
+   "id": "c233aa5f",
    "metadata": {
     "editable": true
    },
@@ -3313,7 +3360,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a89d53a0",
+   "id": "b2b5fa2e",
    "metadata": {
     "editable": true
    },
@@ -3325,7 +3372,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0bdc8b50",
+   "id": "78f014d3",
    "metadata": {
     "editable": true
    },
@@ -3337,7 +3384,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f9edf07c",
+   "id": "a79f4829",
    "metadata": {
     "editable": true
    },
@@ -3349,7 +3396,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1abbdd9c",
+   "id": "43eb2ee4",
    "metadata": {
     "editable": true
    },
@@ -3361,7 +3408,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7b00f144",
+   "id": "805dd5cc",
    "metadata": {
     "editable": true
    },
@@ -3373,7 +3420,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "90a0afbf",
+   "id": "ea389ad8",
    "metadata": {
     "editable": true
    },
@@ -3390,7 +3437,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c4f96471",
+   "id": "29c22980",
    "metadata": {
     "editable": true
    },
@@ -3409,7 +3456,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "26b924de",
+   "id": "15ff24a8",
    "metadata": {
     "editable": true
    },
@@ -3421,7 +3468,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4d98827e",
+   "id": "c2050047",
    "metadata": {
     "editable": true
    },
@@ -3441,7 +3488,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7aff0f96",
+   "id": "d07aa491",
    "metadata": {
     "editable": true
    },
@@ -3479,7 +3526,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8b61c524",
+   "id": "f4eb855c",
    "metadata": {
     "editable": true
    },
@@ -3491,7 +3538,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a605388f",
+   "id": "b2b03e57",
    "metadata": {
     "editable": true
    },
@@ -3501,7 +3548,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5116fd5f",
+   "id": "ffb43d34",
    "metadata": {
     "editable": true
    },
@@ -3513,7 +3560,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b0b06320",
+   "id": "643a528e",
    "metadata": {
     "editable": true
    },
@@ -3524,7 +3571,7 @@
   {
    "cell_type": "code",
    "execution_count": 16,
-   "id": "972ed554",
+   "id": "272fd295",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3569,7 +3616,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ff530d43",
+   "id": "7cdf6f19",
    "metadata": {
     "editable": true
    },
@@ -3586,7 +3633,7 @@
   {
    "cell_type": "code",
    "execution_count": 17,
-   "id": "f9c4b9f9",
+   "id": "dcb74d34",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3614,7 +3661,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5bb16647",
+   "id": "8628fe47",
    "metadata": {
     "editable": true
    },
@@ -3629,7 +3676,7 @@
   {
    "cell_type": "code",
    "execution_count": 18,
-   "id": "f5c25a9a",
+   "id": "f0cf0e3b",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3673,7 +3720,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8691e0f5",
+   "id": "65746580",
    "metadata": {
     "editable": true
    },
@@ -3683,7 +3730,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f5c1a799",
+   "id": "6cb2fa5e",
    "metadata": {
     "editable": true
    },
@@ -3694,7 +3741,7 @@
   {
    "cell_type": "code",
    "execution_count": 19,
-   "id": "7a630992",
+   "id": "09981165",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3722,7 +3769,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5b1de1ef",
+   "id": "06842bac",
    "metadata": {
     "editable": true
    },
@@ -3737,7 +3784,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d6f8533",
+   "id": "d0a00ca6",
    "metadata": {
     "editable": true
    },
@@ -3748,7 +3795,7 @@
   {
    "cell_type": "code",
    "execution_count": 20,
-   "id": "6732b4e4",
+   "id": "b83d619c",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3776,7 +3823,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "903e1d95",
+   "id": "60667807",
    "metadata": {
     "editable": true
    },
@@ -3787,7 +3834,7 @@
   {
    "cell_type": "code",
    "execution_count": 21,
-   "id": "14f83c2d",
+   "id": "e244e18d",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3812,7 +3859,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8a55e3b3",
+   "id": "027aa974",
    "metadata": {
     "editable": true
    },
@@ -3823,7 +3870,7 @@
   {
    "cell_type": "code",
    "execution_count": 22,
-   "id": "c894ef86",
+   "id": "458af951",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3859,7 +3906,7 @@
   {
    "cell_type": "code",
    "execution_count": 23,
-   "id": "83b8201a",
+   "id": "8503a971",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3879,7 +3926,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0f7fe07d",
+   "id": "c161f0c5",
    "metadata": {
     "editable": true
    },
@@ -3890,7 +3937,7 @@
   {
    "cell_type": "code",
    "execution_count": 24,
-   "id": "b1f755f4",
+   "id": "3ef079f8",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3928,7 +3975,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0a1df639",
+   "id": "034338e5",
    "metadata": {
     "editable": true
    },
@@ -3938,7 +3985,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22ea217a",
+   "id": "3d49aee1",
    "metadata": {
     "editable": true
    },
@@ -3952,7 +3999,7 @@
   {
    "cell_type": "code",
    "execution_count": 25,
-   "id": "0dd3c4cb",
+   "id": "20fadbf2",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -3974,7 +4021,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "030639cd",
+   "id": "ab81f79d",
    "metadata": {
     "editable": true
    },
@@ -3984,7 +4031,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "90cc352d",
+   "id": "837788c6",
    "metadata": {
     "editable": true
    },
@@ -3995,7 +4042,7 @@
   {
    "cell_type": "code",
    "execution_count": 26,
-   "id": "40ed6032",
+   "id": "f38c1e61",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4017,7 +4064,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "67e6173f",
+   "id": "6aa5cce6",
    "metadata": {
     "editable": true
    },
@@ -4030,7 +4077,7 @@
   {
    "cell_type": "code",
    "execution_count": 27,
-   "id": "cbfc002f",
+   "id": "c9b0afed",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4055,7 +4102,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dd550ee3",
+   "id": "945e6e5d",
    "metadata": {
     "editable": true
    },
@@ -4067,7 +4114,7 @@
   {
    "cell_type": "code",
    "execution_count": 28,
-   "id": "0ab38cff",
+   "id": "ebaa43ed",
    "metadata": {
     "collapsed": false,
     "editable": true
diff --git a/doc/src/week39/week39.do.txt b/doc/src/week39/week39.do.txt
index bdf1ceb4b..239fd85a7 100644
--- a/doc/src/week39/week39.do.txt
+++ b/doc/src/week39/week39.do.txt
@@ -1164,6 +1164,23 @@ We can easily extend our program to minimize $C_{\text{ridge}}(\beta)$ using gra
 \]
 !et
 
+!split
+===== The Hessian matrix for Ridge Regression =====
+The Hessian matrix of Ridge Regression for our simple example  is given by 
+!bt
+\[
+\bm{H} \equiv \begin{bmatrix}
+\frac{\partial^2 C(\beta)}{\partial \beta_0^2} & \frac{\partial^2 C(\beta)}{\partial \beta_0 \partial \beta_1}  \\
+\frac{\partial^2 C(\beta)}{\partial \beta_0 \partial \beta_1} & \frac{\partial^2 C(\beta)}{\partial \beta_1^2} &  \\
+\end{bmatrix} = \frac{2}{n}X^T X+2\lambda\bm{I}.
+\]
+!et
+This implies that the Hessian matrix  is positive definite, hence the stationary point is a
+minimum.
+Note that the Ridge loss function is convex, as a sum of two convex
+functions. Therefore, the stationary point is a global
+minimum of this function.
+
 
 !split
 ===== Program example for gradient descent with Ridge Regression =====
@@ -1186,14 +1203,21 @@ XT_X = X.T @ X
 
 #Ridge parameter lambda
 lmbda  = 0.001
-Id = lmbda* np.eye(XT_X.shape[0])
+Id = n*lmbda* np.eye(XT_X.shape[0])
+
+# Hessian matrix
+H = (2.0/n)* XT_X+2*lmbda
+# Get the eigenvalues
+EigValues, EigVectors = np.linalg.eig(H)
+print(f"Eigenvalues of Hessian Matrix:{EigValues}")
+
 
 beta_linreg = np.linalg.inv(XT_X+Id) @ X.T @ y
 print(beta_linreg)
 # Start plain gradient descent
 beta = np.random.randn(2,1)
 
-eta = 0.1
+eta = 1.0/np.max(EigValues)
 Niterations = 100
 
 for iter in range(Niterations):