Calculate the QR decomposition of a given matrix using NumPy

In this article, we will discuss QR decomposition of a matrix. QR factorization of a matrix is the decomposition of a matrix say ‘A’ into ‘A=QR’ where Q is orthogonal and R is an upper-triangular matrix. We can calculate the QR decomposition of a given matrix with the help of numpy.linalg.qr(). 

Syntax : numpy.linalg.qr(a, mode=’reduced’)

Parameters :

• a : matrix(M,N) which needs to be factored.
• mode : it is optional. It can be :

Example 1:

Output:

[[1 2 3]
 [3 4 5]]

Q:
 [[-0.31622777 -0.9486833 ]
 [-0.9486833 0.31622777]]

R:
 [[-3.16227766 -4.42718872 -5.69209979]
 [ 0. -0.63245553 -1.26491106]]

Example 2:

Output:

[[1 0]
 [2 4]]

Q:
 [[-0.4472136 -0.89442719]
 [-0.89442719 0.4472136 ]]

R:
 [[-2.23606798 -3.57770876]
 [ 0. 1.78885438]]

Example 3:

Output:

[[ 5 11 -15]
 [ 12 34 -51]
 [-24 -43 92]]

Q:
 [[-0.18318583 -0.08610905 0.97929984]
 [-0.43964598 -0.88381371 -0.15995231]
 [ 0.87929197 -0.45984624 0.12404465]]

R:
 [[-27.29468813 -54.77256208 106.06459346]
 [ 0. -11.22347731 4.06028083]
 [ 0. 0. 4.88017756]]