Book Image

NumPy: Beginner's Guide

By : Ivan Idris
Book Image

NumPy: Beginner's Guide

By: Ivan Idris

Overview of this book

Table of Contents (21 chapters)
NumPy Beginner's Guide Third Edition
About the Author
About the Reviewers
NumPy Functions' References

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:

    [[ 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]]


    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 with the result of the inv() function...