updating text on svd

doc/pub/week35/html/week35-bs.html

@@ -374,7 +374,7 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Sep 3, 2021</h4></center> <!-- date -->
+<center><h4>Sep 4, 2021</h4></center> <!-- date -->
 <br>
 <p>
 

doc/pub/week35/html/week35-reveal.html

@@ -148,7 +148,7 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>&nbsp;<br>
-<center><h4>Sep 3, 2021</h4></center> <!-- date -->
+<center><h4>Sep 4, 2021</h4></center> <!-- date -->
 <br>
 <p>
 
@@ -1673,8 +1673,18 @@ algorithm based on say LU, QR or Cholesky decomposition may lead to singularitie
 There is however a way to partially circumvent this problem and also gain some insights about the ordinary least squares approach, and later shrinkage methods like Ridge and Lasso regressions.
 
 <p>
-This is given by the <b>Singular Value Decomposition</b> algorithm, perhaps
-the most powerful linear algebra algorithm.  Let us look at a
+This is given by the <b>Singular Value Decomposition</b> (SVD) algorithm,
+perhaps the most powerful linear algebra algorithm.  The SVD provides
+a numerically stable matrix decomposition that is used in a large
+swath oc applications and the decomposition is always stable
+numerically.
+
+<p>
+In machine learning it plays a central role in dealing with for example design matrices that may be near singular or singular.
+Furthermore, as we will see here, the singular values can be related to the covariance matrix (and thereby the correlation matrix) and in turn the variance of a given quantity. It plays also an important role in the principal component analysis where high-dimensional data can be reduced to the statistically relevant features.
+
+<p>
+Let us look at a
 different example where we may have problems with the standard matrix
 inversion algorithm. Thereafter we dive into the math of the SVD.
 

doc/pub/week35/html/week35-solarized.html

@@ -300,7 +300,7 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Sep 3, 2021</h4></center> <!-- date -->
+<center><h4>Sep 4, 2021</h4></center> <!-- date -->
 <br>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -1752,8 +1752,18 @@ algorithm based on say LU, QR or Cholesky decomposition may lead to singularitie
 There is however a way to partially circumvent this problem and also gain some insights about the ordinary least squares approach, and later shrinkage methods like Ridge and Lasso regressions.
 
 <p>
-This is given by the <b>Singular Value Decomposition</b> algorithm, perhaps
-the most powerful linear algebra algorithm.  Let us look at a
+This is given by the <b>Singular Value Decomposition</b> (SVD) algorithm,
+perhaps the most powerful linear algebra algorithm.  The SVD provides
+a numerically stable matrix decomposition that is used in a large
+swath oc applications and the decomposition is always stable
+numerically.
+
+<p>
+In machine learning it plays a central role in dealing with for example design matrices that may be near singular or singular.
+Furthermore, as we will see here, the singular values can be related to the covariance matrix (and thereby the correlation matrix) and in turn the variance of a given quantity. It plays also an important role in the principal component analysis where high-dimensional data can be reduced to the statistically relevant features.
+
+<p>
+Let us look at a
 different example where we may have problems with the standard matrix
 inversion algorithm. Thereafter we dive into the math of the SVD.
 

doc/pub/week35/html/week35.html

@@ -305,7 +305,7 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Sep 3, 2021</h4></center> <!-- date -->
+<center><h4>Sep 4, 2021</h4></center> <!-- date -->
 <br>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -1757,8 +1757,18 @@ algorithm based on say LU, QR or Cholesky decomposition may lead to singularitie
 There is however a way to partially circumvent this problem and also gain some insights about the ordinary least squares approach, and later shrinkage methods like Ridge and Lasso regressions.
 
 <p>
-This is given by the <b>Singular Value Decomposition</b> algorithm, perhaps
-the most powerful linear algebra algorithm.  Let us look at a
+This is given by the <b>Singular Value Decomposition</b> (SVD) algorithm,
+perhaps the most powerful linear algebra algorithm.  The SVD provides
+a numerically stable matrix decomposition that is used in a large
+swath oc applications and the decomposition is always stable
+numerically.
+
+<p>
+In machine learning it plays a central role in dealing with for example design matrices that may be near singular or singular.
+Furthermore, as we will see here, the singular values can be related to the covariance matrix (and thereby the correlation matrix) and in turn the variance of a given quantity. It plays also an important role in the principal component analysis where high-dimensional data can be reduced to the statistically relevant features.
+
+<p>
+Let us look at a
 different example where we may have problems with the standard matrix
 inversion algorithm. Thereafter we dive into the math of the SVD.
 

doc/pub/week35/ipynb/week35.ipynb

@@ -10,7 +10,7 @@
     "<!-- Author: -->  \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: **Sep 3, 2021**\n",
+    "Date: **Sep 4, 2021**\n",
     "\n",
     "Copyright 1999-2021, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
     "\n",
@@ -2046,6 +2046,8 @@
    "source": [
     "This serves also as a useful test of our codes. \n",
     "\n",
+    "\n",
+    "\n",
     "## The singular value decomposition\n",
     "\n",
     "\n",
@@ -2065,8 +2067,18 @@
     "\n",
     "There is however a way to partially circumvent this problem and also gain some insights about the ordinary least squares approach, and later shrinkage methods like Ridge and Lasso regressions. \n",
     "\n",
-    "This is given by the **Singular Value Decomposition** algorithm, perhaps\n",
-    "the most powerful linear algebra algorithm.  Let us look at a\n",
+    "This is given by the **Singular Value Decomposition** (SVD) algorithm,\n",
+    "perhaps the most powerful linear algebra algorithm.  The SVD provides\n",
+    "a numerically stable matrix decomposition that is used in a large\n",
+    "swath oc applications and the decomposition is always stable\n",
+    "numerically.\n",
+    "\n",
+    "In machine learning it plays a central role in dealing with for example design matrices that may be near singular or singular.\n",
+    "Furthermore, as we will see here, the singular values can be related to the covariance matrix (and thereby the correlation matrix) and in turn the variance of a given quantity. It plays also an important role in the principal component analysis where high-dimensional data can be reduced to the statistically relevant features. \n",
+    "\n",
+    "\n",
+    "\n",
+    "Let us look at a\n",
     "different example where we may have problems with the standard matrix\n",
     "inversion algorithm. Thereafter we dive into the math of the SVD.\n",
     "\n",

doc/src/week35/week35.do.txt

@@ -1266,6 +1266,8 @@ and we have the obvious case
 
 This serves also as a useful test of our codes. 
 
+
+
 !split
 ===== The singular value decomposition  =====
 
@@ -1287,8 +1289,18 @@ algorithm based on say LU, QR or Cholesky decomposition may lead to singularitie
 
 There is however a way to partially circumvent this problem and also gain some insights about the ordinary least squares approach, and later shrinkage methods like Ridge and Lasso regressions. 
 
-This is given by the _Singular Value Decomposition_ algorithm, perhaps
-the most powerful linear algebra algorithm.  Let us look at a
+This is given by the _Singular Value Decomposition_ (SVD) algorithm,
+perhaps the most powerful linear algebra algorithm.  The SVD provides
+a numerically stable matrix decomposition that is used in a large
+swath oc applications and the decomposition is always stable
+numerically.
+
+In machine learning it plays a central role in dealing with for example design matrices that may be near singular or singular.
+Furthermore, as we will see here, the singular values can be related to the covariance matrix (and thereby the correlation matrix) and in turn the variance of a given quantity. It plays also an important role in the principal component analysis where high-dimensional data can be reduced to the statistically relevant features. 
+
+
+
+Let us look at a
 different example where we may have problems with the standard matrix
 inversion algorithm. Thereafter we dive into the math of the SVD.