Diagonalizing a matrix

In linear algebra, a square matrix A is diagonalizable if it is similar to a diagonal matrix, that is, if there exists an invertible matrix P such that P⁻¹AP is a diagonal matrix.

Diagonalizable matrices and maps are of interest because diagonal matrices are especially easy to handle. If their eigenvalues and eigenvectors are known, one can raise a diagonal matrix to a power by simply raising the diagonal entries to that same power, and the determinant of a diagonal matrix is simply the product of all diagonal entries.

How to do it…

Before getting into the details of checking whether a matrix is diagonalizable or not, let us see how to convert any 1D array into a diagonal matrix.

1. Import the relevant packages:

import numpy as np 

2. Initialize a 1D matrix:

a= np.array([1,2,3]) 

3. Diagonalize the matrix:

np.diag(a)

4. The output of the preceding code is:

array([[1, 0, 0],       [0, 2, 0],       [0, 0, 3]]) 

You should note that all the elements within the one-dimensional array form the...