Time for action – computing the pseudo inverse of a matrix

Let's compute the pseudo inverse of a matrix. Perform the following steps to do so:

1. First, create a matrix as follows:

   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. Calculate the pseudoinverse matrix with the pinv function, as follows:

   pseudoinv = np.linalg.pinv(A)
   print "Pseudo inverse\n", pseudoinv

   The following is the pseudoinverse:

   Pseudo inverse
   [[-0.00555556  0.07222222]
    [ 0.02222222  0.04444444]
    [ 0.05555556 -0.05555556]]
   

3. Multiply the original and pseudoinverse matrices.

   print "Check", A * pseudoinv

   What we get is not an identity matrix, but it comes close to it, as follows:

   Check [[  1.00000000e+00   0.00000000e+00]
    [  8.32667268e-17   1.00000000e+00]]
   

What just happened?

We computed the pseudoinverse of a matrix with the pinv function of the numpy.linalg module. The check by matrix multiplication resulted in a matrix that is approximately an identity matrix...