Time for action – decomposing a matrix

It's time to decompose a matrix with the SVD using the following steps:

1. First, create a matrix as shown in the following:

   A = np.mat("4 11 14;8 7 -2")
   print("A\n", A)

   The matrix we created looks like the following:

   A
   [[ 4 11 14]
    [ 8  7 -2]]
   

2. Decompose the matrix with the svd() function:

   U, Sigma, V = np.linalg.svd(A, full_matrices=False)
   print("U")
   print(U)
   print("Sigma")
   print(Sigma)
   print("V")
   print(V)

   Because of the full_matrices=False specification, NumPy performs a reduced SVD decomposition, which is faster to compute. The result is a tuple containing the two unitary matrices U and V on the left and right, respectively, and the singular values of the middle matrix:

   U
   [[-0.9486833  -0.31622777]
    [-0.31622777  0.9486833 ]]
   Sigma
   [ 18.97366596   9.48683298]
   V
   [[-0.33333333 -0.66666667 -0.66666667]
    [ 0.66666667  0.33333333 -0.66666667]]
   

3. We do not actually have the middle matrix—we only...