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Product of a Matrix and its Transpose Property | Linear Algebra using Python

Linear Algebra using Python | Product of a Matrix and its Transpose Property: Here, we are going to learn about the product of a matrix and its transpose property and its implementation in Python.
Submitted by Anuj Singh, on June 06, 2020

Prerequisites:

• Defining a Matrix
• Transpose Matrix

In linear algebra, an mxn matrix A is multiplied with its transpose A^T then the resultant matrix is symmetric. This is one of the most common ways to generate a symmetric matrix. There is no such restriction for the dimensionality of Matrix A. In this tutorial, we are going to check and verify this property.

A.A^T = S

Where, S is a symmetric matrix

Python code to find the product of a matrix and its transpose property

# Linear Algebra Learning Sequence
# Inverse Property A.AT = S  [AT = transpose of A]

import numpy as np

M = np.array([[2,3,4], [4,4,8], [4,8,7], [4,8,9] ])
print("---Matrix A---\n", M)

pro = np.dot(M,M.T)
print('\n\nProduct of Matrix A with its Transpose : A * AT = I \n\n', pro)

Output:

---Matrix A---
 [[2 3 4]
 [4 4 8]
 [4 8 7]
 [4 8 9]]


Product of Matrix A with its Transpose : A * AT = I 

 [[ 29  52  60  68]
 [ 52  96 104 120]
 [ 60 104 129 143]
 [ 68 120 143 161]]