diff --git a/doc/pub/week48/html/._week48-bs006.html b/doc/pub/week48/html/._week48-bs006.html
index 5a086a8d8..703810d96 100644
--- a/doc/pub/week48/html/._week48-bs006.html
+++ b/doc/pub/week48/html/._week48-bs006.html
@@ -261,9 +261,9 @@ MathJax.Hub.Config({
 <h2 id="___sec5" class="anchor">The equations </h2>
 
 <p>
-Suppose we define a polynomial transformation of degree two only (we continue to live in a plane with \( x_i \) and \( y_i \) as variables)
+Suppose we define a polynomial transformation of degree two only (we continue to live in a plane with \( x_i \) and \( y_i \) as variables). We define a vector \( \boldsymbol{x}_i=[x_i,y_i] \) and have
 $$
-z = \phi(x_i) =\left(1, \sqrt{2}x_i, \sqrt{2}y_i, x_i^2, y_i^2, \sqrt{2}x_iy_i\right).
+\boldsymbol{z}_i = \phi(\boldsymbol{x}_i)^T =\left(1, \sqrt{2}x_i, \sqrt{2}y_i, x_i^2, y_i^2, \sqrt{2}x_iy_i\right).
 $$
 
 <p>
@@ -291,10 +291,10 @@ $$
 <p>
 We note that this dot product can be rewritten as
 $$
-K(\boldsymbol{x}_i,\boldsymbol{x}_j)=[1+\boldsymbol{x}^T\boldsymbol{x}']^d,
+K(\boldsymbol{x}_i,\boldsymbol{x}_j)=[1+\boldsymbol{x}_i^T\boldsymbol{x}_j]^d,
 $$
 
-where \( d=2 \) in our case and \( \boldsymbol{x}=[x_i,y_i] \) and \( \boldsymbol{x}=[x_j,y_j] \).
+where \( d=2 \) in our case and \( \boldsymbol{x}_i=[x_i,y_i] \) and \( \boldsymbol{x}_j=[x_j,y_j] \).
 To compute the last equation is however inefficient from a computational stand.
 Instead of computing the last equation for the kernel, we simply compute
 the dot product \( (\boldsymbol{x}_i^T\boldsymbol{x}_j)^2 \).
diff --git a/doc/pub/week48/html/._week48-bs015.html b/doc/pub/week48/html/._week48-bs015.html
index fa35d4a8c..2f2a0ee84 100644
--- a/doc/pub/week48/html/._week48-bs015.html
+++ b/doc/pub/week48/html/._week48-bs015.html
@@ -273,14 +273,11 @@ $$
 <ol>
 <li> With a given kernel we can thus define the matrix \( \boldsymbol{P} \).</li>
 <li> The matrix \( \boldsymbol{P} \) has matrix elements \( p_{ij}=y_iy_jK(\boldsymbol{x}_i,\boldsymbol{x}_j) \). Given a kernel \( K \) and the targets \( y_i \) this matrix is easy to set up.</li>
-<li> The \( \boldsymbol{q} \) is zero.</li>
+<li> The vector \( \boldsymbol{q} \) is zero.</li>
 <li> The constraint \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \) leads to \( f=0 \) and \( \boldsymbol{A}=\boldsymbol{y} \).</li>
-<li> To set up the matrix \( \boldsymbol{G} \) we note that the inequalities \( 0\leq \lambda_i \leq C \) can be split up into</li>
+<li> To set up the matrix \( \boldsymbol{G} \) we note that the inequalities \( 0\leq \lambda_i \leq C \) can be split up into \( 0\leq \lambda_i \) and \( \lambda_i \leq C \). These two inequalities define then the matrix \( \boldsymbol{G} \) and the vector \( \boldsymbol{h} \).</li>
 </ol>
 
-\( 0\leq \lambda_i \) and \( \lambda_i \leq C \). These two inequalities define then the matrix \( \boldsymbol{G} \) and the vector \( \boldsymbol{h} \).
-
-<p>
 <p>
 <!-- navigation buttons at the bottom of the page -->
 <ul class="pagination">
diff --git a/doc/pub/week48/html/._week48-bs016.html b/doc/pub/week48/html/._week48-bs016.html
index c57531835..65d6a6344 100644
--- a/doc/pub/week48/html/._week48-bs016.html
+++ b/doc/pub/week48/html/._week48-bs016.html
@@ -270,18 +270,18 @@ $$
 0& 0 & -1 & \dots & 0 \\
 \dots& \dots & \dots  & \dots & \dots \\
 0& 0 & 0 & \dots & -1 \\
- -& 0 & 0 & \dots & 0 \\
+1 & 0 & 0 & \dots & 0 \\
 0& 1 & 0 & \dots & 0 \\
 0& 0 & 1 & \dots & 0 \\
 \dots& \dots & \dots  & \dots & \dots \\
 0& 0 & 0 & \dots & 1 \\
-\end{bmatrix}\boldsymbol{\lambda}
+\end{bmatrix}
 \begin{bmatrix} \lambda_1 \\
 \lambda_2 \\
 \lambda_3 \\
 \dots \\
 \lambda_n \\
-\end{bmatrix}\boldsymbol{\lambda}=
+\end{bmatrix}=
 \begin{bmatrix} 0 \\
 0 \\
 0 \\
@@ -292,7 +292,7 @@ C \\
 C \\
 \dots \\
 C \\
-\end{bmatrix}\boldsymbol{\lambda}
+\end{bmatrix}.
 $$
 
 <p>
diff --git a/doc/pub/week48/html/week48-reveal.html b/doc/pub/week48/html/week48-reveal.html
index ebcfa4cd8..7bdb8c9c1 100644
--- a/doc/pub/week48/html/week48-reveal.html
+++ b/doc/pub/week48/html/week48-reveal.html
@@ -294,10 +294,10 @@ plt.show()
 <h2 id="___sec5">The equations </h2>
 
 <p>
-Suppose we define a polynomial transformation of degree two only (we continue to live in a plane with \( x_i \) and \( y_i \) as variables)
+Suppose we define a polynomial transformation of degree two only (we continue to live in a plane with \( x_i \) and \( y_i \) as variables). We define a vector \( \boldsymbol{x}_i=[x_i,y_i] \) and have
 <p>&nbsp;<br>
 $$
-z = \phi(x_i) =\left(1, \sqrt{2}x_i, \sqrt{2}y_i, x_i^2, y_i^2, \sqrt{2}x_iy_i\right).
+\boldsymbol{z}_i = \phi(\boldsymbol{x}_i)^T =\left(1, \sqrt{2}x_i, \sqrt{2}y_i, x_i^2, y_i^2, \sqrt{2}x_iy_i\right).
 $$
 <p>&nbsp;<br>
 
@@ -335,11 +335,11 @@ $$
 We note that this dot product can be rewritten as
 <p>&nbsp;<br>
 $$
-K(\boldsymbol{x}_i,\boldsymbol{x}_j)=[1+\boldsymbol{x}^T\boldsymbol{x}']^d,
+K(\boldsymbol{x}_i,\boldsymbol{x}_j)=[1+\boldsymbol{x}_i^T\boldsymbol{x}_j]^d,
 $$
 <p>&nbsp;<br>
 
-where \( d=2 \) in our case and \( \boldsymbol{x}=[x_i,y_i] \) and \( \boldsymbol{x}=[x_j,y_j] \).
+where \( d=2 \) in our case and \( \boldsymbol{x}_i=[x_i,y_i] \) and \( \boldsymbol{x}_j=[x_j,y_j] \).
 To compute the last equation is however inefficient from a computational stand.
 Instead of computing the last equation for the kernel, we simply compute
 the dot product \( (\boldsymbol{x}_i^T\boldsymbol{x}_j)^2 \).
@@ -809,13 +809,10 @@ $$
 <ol>
 <p><li> With a given kernel we can thus define the matrix \( \boldsymbol{P} \).</li>
 <p><li> The matrix \( \boldsymbol{P} \) has matrix elements \( p_{ij}=y_iy_jK(\boldsymbol{x}_i,\boldsymbol{x}_j) \). Given a kernel \( K \) and the targets \( y_i \) this matrix is easy to set up.</li>
-<p><li> The \( \boldsymbol{q} \) is zero.</li>
+<p><li> The vector \( \boldsymbol{q} \) is zero.</li>
 <p><li> The constraint \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \) leads to \( f=0 \) and \( \boldsymbol{A}=\boldsymbol{y} \).</li>
-<p><li> To set up the matrix \( \boldsymbol{G} \) we note that the inequalities \( 0\leq \lambda_i \leq C \) can be split up into</li>
+<p><li> To set up the matrix \( \boldsymbol{G} \) we note that the inequalities \( 0\leq \lambda_i \leq C \) can be split up into \( 0\leq \lambda_i \) and \( \lambda_i \leq C \). These two inequalities define then the matrix \( \boldsymbol{G} \) and the vector \( \boldsymbol{h} \).</li>
 </ol>
-<p>
-
-\( 0\leq \lambda_i \) and \( \lambda_i \leq C \). These two inequalities define then the matrix \( \boldsymbol{G} \) and the vector \( \boldsymbol{h} \).
 </section>
 
 
@@ -833,18 +830,18 @@ $$
 0& 0 & -1 & \dots & 0 \\
 \dots& \dots & \dots  & \dots & \dots \\
 0& 0 & 0 & \dots & -1 \\
- -& 0 & 0 & \dots & 0 \\
+1 & 0 & 0 & \dots & 0 \\
 0& 1 & 0 & \dots & 0 \\
 0& 0 & 1 & \dots & 0 \\
 \dots& \dots & \dots  & \dots & \dots \\
 0& 0 & 0 & \dots & 1 \\
-\end{bmatrix}\boldsymbol{\lambda}
+\end{bmatrix}
 \begin{bmatrix} \lambda_1 \\
 \lambda_2 \\
 \lambda_3 \\
 \dots \\
 \lambda_n \\
-\end{bmatrix}\boldsymbol{\lambda}=
+\end{bmatrix}=
 \begin{bmatrix} 0 \\
 0 \\
 0 \\
@@ -855,7 +852,7 @@ C \\
 C \\
 \dots \\
 C \\
-\end{bmatrix}\boldsymbol{\lambda}
+\end{bmatrix}.
 $$
 <p>&nbsp;<br>
 
diff --git a/doc/pub/week48/html/week48-solarized.html b/doc/pub/week48/html/week48-solarized.html
index 873e0e3b9..026699991 100644
--- a/doc/pub/week48/html/week48-solarized.html
+++ b/doc/pub/week48/html/week48-solarized.html
@@ -342,9 +342,9 @@ plt.show()
 <h2 id="___sec5">The equations </h2>
 
 <p>
-Suppose we define a polynomial transformation of degree two only (we continue to live in a plane with \( x_i \) and \( y_i \) as variables)
+Suppose we define a polynomial transformation of degree two only (we continue to live in a plane with \( x_i \) and \( y_i \) as variables). We define a vector \( \boldsymbol{x}_i=[x_i,y_i] \) and have
 $$
-z = \phi(x_i) =\left(1, \sqrt{2}x_i, \sqrt{2}y_i, x_i^2, y_i^2, \sqrt{2}x_iy_i\right).
+\boldsymbol{z}_i = \phi(\boldsymbol{x}_i)^T =\left(1, \sqrt{2}x_i, \sqrt{2}y_i, x_i^2, y_i^2, \sqrt{2}x_iy_i\right).
 $$
 
 <p>
@@ -372,10 +372,10 @@ $$
 <p>
 We note that this dot product can be rewritten as
 $$
-K(\boldsymbol{x}_i,\boldsymbol{x}_j)=[1+\boldsymbol{x}^T\boldsymbol{x}']^d,
+K(\boldsymbol{x}_i,\boldsymbol{x}_j)=[1+\boldsymbol{x}_i^T\boldsymbol{x}_j]^d,
 $$
 
-where \( d=2 \) in our case and \( \boldsymbol{x}=[x_i,y_i] \) and \( \boldsymbol{x}=[x_j,y_j] \).
+where \( d=2 \) in our case and \( \boldsymbol{x}_i=[x_i,y_i] \) and \( \boldsymbol{x}_j=[x_j,y_j] \).
 To compute the last equation is however inefficient from a computational stand.
 Instead of computing the last equation for the kernel, we simply compute
 the dot product \( (\boldsymbol{x}_i^T\boldsymbol{x}_j)^2 \).
@@ -816,14 +816,11 @@ $$
 <ol>
 <li> With a given kernel we can thus define the matrix \( \boldsymbol{P} \).</li>
 <li> The matrix \( \boldsymbol{P} \) has matrix elements \( p_{ij}=y_iy_jK(\boldsymbol{x}_i,\boldsymbol{x}_j) \). Given a kernel \( K \) and the targets \( y_i \) this matrix is easy to set up.</li>
-<li> The \( \boldsymbol{q} \) is zero.</li>
+<li> The vector \( \boldsymbol{q} \) is zero.</li>
 <li> The constraint \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \) leads to \( f=0 \) and \( \boldsymbol{A}=\boldsymbol{y} \).</li>
-<li> To set up the matrix \( \boldsymbol{G} \) we note that the inequalities \( 0\leq \lambda_i \leq C \) can be split up into</li>
+<li> To set up the matrix \( \boldsymbol{G} \) we note that the inequalities \( 0\leq \lambda_i \leq C \) can be split up into \( 0\leq \lambda_i \) and \( \lambda_i \leq C \). These two inequalities define then the matrix \( \boldsymbol{G} \) and the vector \( \boldsymbol{h} \).</li>
 </ol>
 
-\( 0\leq \lambda_i \) and \( \lambda_i \leq C \). These two inequalities define then the matrix \( \boldsymbol{G} \) and the vector \( \boldsymbol{h} \).
-
-<p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
 <h2 id="___sec15">Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \) </h2>
@@ -838,18 +835,18 @@ $$
 0& 0 & -1 & \dots & 0 \\
 \dots& \dots & \dots  & \dots & \dots \\
 0& 0 & 0 & \dots & -1 \\
- -& 0 & 0 & \dots & 0 \\
+1 & 0 & 0 & \dots & 0 \\
 0& 1 & 0 & \dots & 0 \\
 0& 0 & 1 & \dots & 0 \\
 \dots& \dots & \dots  & \dots & \dots \\
 0& 0 & 0 & \dots & 1 \\
-\end{bmatrix}\boldsymbol{\lambda}
+\end{bmatrix}
 \begin{bmatrix} \lambda_1 \\
 \lambda_2 \\
 \lambda_3 \\
 \dots \\
 \lambda_n \\
-\end{bmatrix}\boldsymbol{\lambda}=
+\end{bmatrix}=
 \begin{bmatrix} 0 \\
 0 \\
 0 \\
@@ -860,7 +857,7 @@ C \\
 C \\
 \dots \\
 C \\
-\end{bmatrix}\boldsymbol{\lambda}
+\end{bmatrix}.
 $$
 
 <p>
diff --git a/doc/pub/week48/html/week48.html b/doc/pub/week48/html/week48.html
index 2b26fdf3d..be0846702 100644
--- a/doc/pub/week48/html/week48.html
+++ b/doc/pub/week48/html/week48.html
@@ -347,9 +347,9 @@ plt<span style="color: #666666">.</span>show()
 <h2 id="___sec5">The equations </h2>
 
 <p>
-Suppose we define a polynomial transformation of degree two only (we continue to live in a plane with \( x_i \) and \( y_i \) as variables)
+Suppose we define a polynomial transformation of degree two only (we continue to live in a plane with \( x_i \) and \( y_i \) as variables). We define a vector \( \boldsymbol{x}_i=[x_i,y_i] \) and have
 $$
-z = \phi(x_i) =\left(1, \sqrt{2}x_i, \sqrt{2}y_i, x_i^2, y_i^2, \sqrt{2}x_iy_i\right).
+\boldsymbol{z}_i = \phi(\boldsymbol{x}_i)^T =\left(1, \sqrt{2}x_i, \sqrt{2}y_i, x_i^2, y_i^2, \sqrt{2}x_iy_i\right).
 $$
 
 <p>
@@ -377,10 +377,10 @@ $$
 <p>
 We note that this dot product can be rewritten as
 $$
-K(\boldsymbol{x}_i,\boldsymbol{x}_j)=[1+\boldsymbol{x}^T\boldsymbol{x}']^d,
+K(\boldsymbol{x}_i,\boldsymbol{x}_j)=[1+\boldsymbol{x}_i^T\boldsymbol{x}_j]^d,
 $$
 
-where \( d=2 \) in our case and \( \boldsymbol{x}=[x_i,y_i] \) and \( \boldsymbol{x}=[x_j,y_j] \).
+where \( d=2 \) in our case and \( \boldsymbol{x}_i=[x_i,y_i] \) and \( \boldsymbol{x}_j=[x_j,y_j] \).
 To compute the last equation is however inefficient from a computational stand.
 Instead of computing the last equation for the kernel, we simply compute
 the dot product \( (\boldsymbol{x}_i^T\boldsymbol{x}_j)^2 \).
@@ -821,14 +821,11 @@ $$
 <ol>
 <li> With a given kernel we can thus define the matrix \( \boldsymbol{P} \).</li>
 <li> The matrix \( \boldsymbol{P} \) has matrix elements \( p_{ij}=y_iy_jK(\boldsymbol{x}_i,\boldsymbol{x}_j) \). Given a kernel \( K \) and the targets \( y_i \) this matrix is easy to set up.</li>
-<li> The \( \boldsymbol{q} \) is zero.</li>
+<li> The vector \( \boldsymbol{q} \) is zero.</li>
 <li> The constraint \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \) leads to \( f=0 \) and \( \boldsymbol{A}=\boldsymbol{y} \).</li>
-<li> To set up the matrix \( \boldsymbol{G} \) we note that the inequalities \( 0\leq \lambda_i \leq C \) can be split up into</li>
+<li> To set up the matrix \( \boldsymbol{G} \) we note that the inequalities \( 0\leq \lambda_i \leq C \) can be split up into \( 0\leq \lambda_i \) and \( \lambda_i \leq C \). These two inequalities define then the matrix \( \boldsymbol{G} \) and the vector \( \boldsymbol{h} \).</li>
 </ol>
 
-\( 0\leq \lambda_i \) and \( \lambda_i \leq C \). These two inequalities define then the matrix \( \boldsymbol{G} \) and the vector \( \boldsymbol{h} \).
-
-<p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
 <h2 id="___sec15">Setting up \( \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \) </h2>
@@ -843,18 +840,18 @@ $$
 0& 0 & -1 & \dots & 0 \\
 \dots& \dots & \dots  & \dots & \dots \\
 0& 0 & 0 & \dots & -1 \\
- -& 0 & 0 & \dots & 0 \\
+1 & 0 & 0 & \dots & 0 \\
 0& 1 & 0 & \dots & 0 \\
 0& 0 & 1 & \dots & 0 \\
 \dots& \dots & \dots  & \dots & \dots \\
 0& 0 & 0 & \dots & 1 \\
-\end{bmatrix}\boldsymbol{\lambda}
+\end{bmatrix}
 \begin{bmatrix} \lambda_1 \\
 \lambda_2 \\
 \lambda_3 \\
 \dots \\
 \lambda_n \\
-\end{bmatrix}\boldsymbol{\lambda}=
+\end{bmatrix}=
 \begin{bmatrix} 0 \\
 0 \\
 0 \\
@@ -865,7 +862,7 @@ C \\
 C \\
 \dots \\
 C \\
-\end{bmatrix}\boldsymbol{\lambda}
+\end{bmatrix}.
 $$
 
 <p>
diff --git a/doc/pub/week48/ipynb/ipynb-week48-src.tar.gz b/doc/pub/week48/ipynb/ipynb-week48-src.tar.gz
index 3adffd050..f1c2daebe 100644
Binary files a/doc/pub/week48/ipynb/ipynb-week48-src.tar.gz and b/doc/pub/week48/ipynb/ipynb-week48-src.tar.gz differ
diff --git a/doc/pub/week48/ipynb/week48.ipynb b/doc/pub/week48/ipynb/week48.ipynb
index 65b1ea189..5dd1f2f42 100644
--- a/doc/pub/week48/ipynb/week48.ipynb
+++ b/doc/pub/week48/ipynb/week48.ipynb
@@ -138,7 +138,7 @@
    "source": [
     "## The equations\n",
     "\n",
-    "Suppose we define a polynomial transformation of degree two only (we continue to live in a plane with $x_i$ and $y_i$ as variables)"
+    "Suppose we define a polynomial transformation of degree two only (we continue to live in a plane with $x_i$ and $y_i$ as variables). We define a vector $\\boldsymbol{x}_i=[x_i,y_i]$ and have"
    ]
   },
   {
@@ -146,7 +146,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "z = \\phi(x_i) =\\left(1, \\sqrt{2}x_i, \\sqrt{2}y_i, x_i^2, y_i^2, \\sqrt{2}x_iy_i\\right).\n",
+    "\\boldsymbol{z}_i = \\phi(\\boldsymbol{x}_i)^T =\\left(1, \\sqrt{2}x_i, \\sqrt{2}y_i, x_i^2, y_i^2, \\sqrt{2}x_iy_i\\right).\n",
     "$$"
    ]
   },
@@ -227,7 +227,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "K(\\boldsymbol{x}_i,\\boldsymbol{x}_j)=[1+\\boldsymbol{x}^T\\boldsymbol{x}']^d,\n",
+    "K(\\boldsymbol{x}_i,\\boldsymbol{x}_j)=[1+\\boldsymbol{x}_i^T\\boldsymbol{x}_j]^d,\n",
     "$$"
    ]
   },
@@ -235,7 +235,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "where $d=2$ in our case and $\\boldsymbol{x}=[x_i,y_i]$ and $\\boldsymbol{x}=[x_j,y_j]$.\n",
+    "where $d=2$ in our case and $\\boldsymbol{x}_i=[x_i,y_i]$ and $\\boldsymbol{x}_j=[x_j,y_j]$.\n",
     "To compute the last equation is however inefficient from a computational stand.\n",
     "Instead of computing the last equation for the kernel, we simply compute\n",
     "the dot product $(\\boldsymbol{x}_i^T\\boldsymbol{x}_j)^2$.\n",
@@ -815,13 +815,11 @@
     "\n",
     "2. The matrix $\\boldsymbol{P}$ has matrix elements $p_{ij}=y_iy_jK(\\boldsymbol{x}_i,\\boldsymbol{x}_j)$. Given a kernel $K$ and the targets $y_i$ this matrix is easy to set up.\n",
     "\n",
-    "3. The $\\boldsymbol{q}$ is zero.\n",
+    "3. The vector $\\boldsymbol{q}$ is zero.\n",
     "\n",
     "4. The constraint $\\boldsymbol{y}^T\\boldsymbol{\\lambda}=0$ leads to $f=0$ and $\\boldsymbol{A}=\\boldsymbol{y}$.\n",
     "\n",
-    "5. To set up the matrix $\\boldsymbol{G}$ we note that the inequalities $0\\leq \\lambda_i \\leq C$ can be split up into\n",
-    "\n",
-    "$0\\leq \\lambda_i$ and $\\lambda_i \\leq C$. These two inequalities define then the matrix $\\boldsymbol{G}$ and the vector $\\boldsymbol{h}$.\n",
+    "5. To set up the matrix $\\boldsymbol{G}$ we note that the inequalities $0\\leq \\lambda_i \\leq C$ can be split up into $0\\leq \\lambda_i$ and $\\lambda_i \\leq C$. These two inequalities define then the matrix $\\boldsymbol{G}$ and the vector $\\boldsymbol{h}$.\n",
     "\n",
     "## Setting up $\\boldsymbol{G}\\boldsymbol{\\lambda} \\preceq \\boldsymbol{h}$\n",
     "\n",
@@ -840,18 +838,18 @@
     "0& 0 & -1 & \\dots & 0 \\\\\n",
     "\\dots& \\dots & \\dots  & \\dots & \\dots \\\\\n",
     "0& 0 & 0 & \\dots & -1 \\\\\n",
-    " -& 0 & 0 & \\dots & 0 \\\\\n",
+    "1 & 0 & 0 & \\dots & 0 \\\\\n",
     "0& 1 & 0 & \\dots & 0 \\\\\n",
     "0& 0 & 1 & \\dots & 0 \\\\\n",
     "\\dots& \\dots & \\dots  & \\dots & \\dots \\\\\n",
     "0& 0 & 0 & \\dots & 1 \\\\\n",
-    "\\end{bmatrix}\\boldsymbol{\\lambda}\n",
+    "\\end{bmatrix}\n",
     "\\begin{bmatrix} \\lambda_1 \\\\\n",
     "\\lambda_2 \\\\\n",
     "\\lambda_3 \\\\\n",
     "\\dots \\\\\n",
     "\\lambda_n \\\\\n",
-    "\\end{bmatrix}\\boldsymbol{\\lambda}=\n",
+    "\\end{bmatrix}=\n",
     "\\begin{bmatrix} 0 \\\\\n",
     "0 \\\\\n",
     "0 \\\\\n",
@@ -862,7 +860,7 @@
     "C \\\\\n",
     "\\dots \\\\\n",
     "C \\\\\n",
-    "\\end{bmatrix}\\boldsymbol{\\lambda}\n",
+    "\\end{bmatrix}.\n",
     "$$"
    ]
   },
diff --git a/doc/src/week48/week48.do.txt b/doc/src/week48/week48.do.txt
index 3209ff18b..3f1006fe2 100644
--- a/doc/src/week48/week48.do.txt
+++ b/doc/src/week48/week48.do.txt
@@ -119,10 +119,10 @@ plt.show()
 !split
 ===== The equations =====
 
-Suppose we define a polynomial transformation of degree two only (we continue to live in a plane with $x_i$ and $y_i$ as variables)
+Suppose we define a polynomial transformation of degree two only (we continue to live in a plane with $x_i$ and $y_i$ as variables). We define a vector $\bm{x}_i=[x_i,y_i]$ and have
 !bt
 \[
-z = \phi(x_i) =\left(1, \sqrt{2}x_i, \sqrt{2}y_i, x_i^2, y_i^2, \sqrt{2}x_iy_i\right).
+\bm{z}_i = \phi(\bm{x}_i)^T =\left(1, \sqrt{2}x_i, \sqrt{2}y_i, x_i^2, y_i^2, \sqrt{2}x_iy_i\right).
 \]
 !et
 
@@ -155,10 +155,10 @@ K(\bm{x}_i,\bm{x}_j)=[1, \sqrt{2}x_i, \sqrt{2}y_i, x_i^2, y_i^2, \sqrt{2}x_iy_i]
 We note that this dot product can be rewritten as
 !bt
 \[
-K(\bm{x}_i,\bm{x}_j)=[1+\bm{x}^T\bm{x}']^d,
+K(\bm{x}_i,\bm{x}_j)=[1+\bm{x}_i^T\bm{x}_j]^d,
 \]
 !et
-where $d=2$ in our case and $\bm{x}=[x_i,y_i]$ and $\bm{x}=[x_j,y_j]$.
+where $d=2$ in our case and $\bm{x}_i=[x_i,y_i]$ and $\bm{x}_j=[x_j,y_j]$.
 To compute the last equation is however inefficient from a computational stand.
 Instead of computing the last equation for the kernel, we simply compute
 the dot product $(\bm{x}_i^T\bm{x}_j)^2$.
@@ -574,10 +574,9 @@ We have the general problem
 
 o With a given kernel we can thus define the matrix $\bm{P}$.
 o The matrix $\bm{P}$ has matrix elements $p_{ij}=y_iy_jK(\bm{x}_i,\bm{x}_j)$. Given a kernel $K$ and the targets $y_i$ this matrix is easy to set up.
-o The $\bm{q}$ is zero.
+o The vector $\bm{q}$ is zero.
 o The constraint $\bm{y}^T\bm{\lambda}=0$ leads to $f=0$ and $\bm{A}=\bm{y}$.
-o To set up the matrix $\bm{G}$ we note that the inequalities $0\leq \lambda_i \leq C$ can be split up into
-$0\leq \lambda_i$ and $\lambda_i \leq C$. These two inequalities define then the matrix $\bm{G}$ and the vector $\bm{h}$.
+o To set up the matrix $\bm{G}$ we note that the inequalities $0\leq \lambda_i \leq C$ can be split up into $0\leq \lambda_i$ and $\lambda_i \leq C$. These two inequalities define then the matrix $\bm{G}$ and the vector $\bm{h}$.
 
 !split
 =====  Setting up $\bm{G}\bm{\lambda} \preceq \bm{h}$ =====
@@ -592,18 +591,18 @@ can be written as
 0& 0 & -1 & \dots & 0 \\
 \dots& \dots & \dots  & \dots & \dots \\
 0& 0 & 0 & \dots & -1 \\
- -& 0 & 0 & \dots & 0 \\
+1 & 0 & 0 & \dots & 0 \\
 0& 1 & 0 & \dots & 0 \\
 0& 0 & 1 & \dots & 0 \\
 \dots& \dots & \dots  & \dots & \dots \\
 0& 0 & 0 & \dots & 1 \\
-\end{bmatrix}\bm{\lambda}
+\end{bmatrix}
 \begin{bmatrix} \lambda_1 \\
 \lambda_2 \\
 \lambda_3 \\
 \dots \\
 \lambda_n \\
-\end{bmatrix}\bm{\lambda}=
+\end{bmatrix}=
 \begin{bmatrix} 0 \\
 0 \\
 0 \\
@@ -614,7 +613,7 @@ C \\
 C \\
 \dots \\
 C \\
-\end{bmatrix}\bm{\lambda}
+\end{bmatrix}.
 \]
 !et