Added material to slides

doc/src/Regression/Regression.do.txt

@@ -1590,9 +1590,14 @@ def SVDinv(A):
     numpy and scipy.linalg at the cost of being slower.
     '''
     U, s, VT = np.linalg.svd(A)
+#    print('test U')
+#    print( (np.transpose(U) @ U - U @np.transpose(U)))
+#    print('test VT')
+#    print( (np.transpose(VT) @ VT - VT @np.transpose(VT)))
     print(U)
     print(s)
     print(VT)
+
     D = np.zeros((len(U),len(VT)))
     for i in range(0,len(VT)):
         D[i,i]=s[i]
@@ -1652,7 +1657,7 @@ We have our design matrix
 with $\bm{U}\in {\mathbb{R}}^{n\times n}$, $\bm{\Sigma}\in {\mathbb{R}}^{n\times p}$
 and $\bm{V}\in {\mathbb{R}}^{p\times p}$.
 
-We have $\bm{U}^T\bm{U}=\bm{I}$ and $\bm{V}^T\bm{V}=\bm{V}\bm{V}^T=\bm{I}$.
+The matrices $\bm{U}$ and $\bm{V}$ are unitary/orthonormal matrices, that is in case the matrices are real we have $\bm{U}^T\bm{U}=\bm{U}\bm{U}^T=\bm{I}$ and $\bm{V}^T\bm{V}=\bm{V}\bm{V}^T=\bm{I}$.
 
 !split
 ===== Spectral Decomposition of the OLS =====