Calculating the QR decomposition of a matrix

Similar to the LU decomposition, QR decomposition is the decomposition of an original matrix into its constituent parts.

In this particular case, the matrix A = QR, where Q is an orthogonal matrix and R is an upper triangular matrix.

Before getting into further details, let us look into the properties of an orthogonal matrix:

• It is a square matrix
• Multiplying Q with its transpose results in an identity matrix 

How to do it…

QR decomposition can be done by using the qr function within scipy.linalg.

In the following code, let us look into how QR decomposition works:

1. Load the relevant packages:

import scipy.linalg as linalg
import numpy as np 

2. Initialize a matrix:

A = np.array([ [2., 1., 1.], [1., 3., 2.], [1., 0., 0]]) 

3. Extract the Q and R matrices of the matrix A:

Q, R = linalg.qr(A) 

4. Check the output values:

print(Q)
[[-0.81649658  0.27602622 -0.50709255]
[-0.40824829 -0.89708523  0.16903085]
[-0.40824829  0.34503278  0.84515425]] 
print(R)
[[-2.44948974 -2...