Time for action – inverting matrices

The inverse of a matrix A in linear algebra is the matrix A-1, which, when multiplied with the original matrix, is equal to the identity matrix I. This can be written as follows:

A A-1 = I

The inv() function in the numpy.linalg package can invert an example matrix with the following steps:

1. Create the example matrix with the mat() function we used in the previous chapters:

   A = np.mat("0 1 2;1 0 3;4 -3 8")
   print("A\n", A)

   The A matrix appears as follows:

   A
   [[ 0  1  2]
    [ 1  0  3]
    [ 4 -3  8]]
   

2. Invert the matrix with the inv() function:

   inverse = np.linalg.inv(A)
   print("inverse of A\n", inverse)

   The inverse matrix appears as follows:

   inverse of A
   [[-4.5  7.  -1.5]
    [-2.   4.  -1. ]
    [ 1.5 -2.   0.5]]
   

   Tip

   If the matrix is singular, or not square, a LinAlgError is raised. If you want, you can check the result manually with a pen and paper. This is left as an exercise for the reader.

3. Check the result by multiplying the original matrix...