Get the QR factorization of a given NumPy array Last Updated : 29 Aug, 2020 Comments Improve Suggest changes Like Article Like Report In this article, we will discuss QR decomposition or QR factorization 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 factorize the matrix using numpy.linalg.qr() function. Syntax : numpy.linalg.qr(a, mode='reduced') Parameters : a : matrix(M,N) which needs to be factored.mode : it is optional. It can be : Below are some examples of how to use the above-described function : Example 1: QR factorization of 2X2 matrix Python3 # Import numpy package import numpy as np # Create a numpy array arr = np.array([[10,22],[13,6]]) # Find the QR factor of array q, r = np.linalg.qr(arr) # Print the result print("Decomposition of matrix:") print( "q=\n", q, "\nr=\n", r) Output : Example 2: QR factorization of 2X4 matrix Python3 # Import numpy package import numpy as np # Create a numpy array arr = np.array([[0, 1], [1, 0], [1, 1], [2, 2]]) # Find the QR factor of array q, r = np.linalg.qr(arr) # Print the result print("Decomposition of matrix:") print( "q=\n", q, "\nr=\n", r) Output : Example 3: QR factorization of 3X3 matrix Python3 # Import numpy package import numpy as np # Create a numpy array arr = np.array([[5, 11, -15], [12, 34, -51], [-24, -43, 92]], dtype=np.int32) # Find the QR factor of array q, r = np.linalg.qr(arr) # Print the result print("Decomposition of matrix:") print( "q=\n", q, "\nr=\n", r) Output : Comment More info P priyabisht Follow Improve Article Tags : Numpy Python-numpy Python numpy-Linear Algebra Explore NumPy Tutorial - Python Library 3 min read IntroductionNumPy Introduction 7 min read Python NumPy 6 min read NumPy Array in Python 2 min read Basics of NumPy Arrays 4 min read Numpy - ndarray 3 min read Data type Object (dtype) in NumPy Python 3 min read Creating NumPy ArrayNumpy - Array Creation 5 min read numpy.arange() in Python 2 min read numpy.zeros() in Python 2 min read NumPy - Create array filled with all ones 2 min read NumPy - linspace() Function 2 min read numpy.eye() in Python 2 min read Creating a one-dimensional NumPy array 2 min read How to create an empty and a full NumPy array 2 min read Create a Numpy array filled with all zeros - Python 2 min read How to generate 2-D Gaussian array using NumPy? 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