updating text on svd

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. 
 
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+
 !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.