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Sum of Symmetric Matrices | Linear Algebra using Python

Linear Algebra using Python | Sum of Symmetric Matrices: Here, we are going to learn about the sum of symmetric matrices and its implementation in Python.
Submitted by Anuj Singh, on June 13, 2020

Prerequisite:

• Defining Matrix using Numpy
• Symmetric Matrices

Here, we will learn how to create two symmetric matrices and will add them? Adding two symmetric matrices results in a symmetric matrix.

S₀ = S₁ + S₂

Note: The dimensions of S₁ and S₂ are same!

Example:

Python code to find sum of symmetric matrices

# Linear Algebra Learning Sequence
# Addition of two symmetric Matrix

import numpy as np

M1 = np.array([[2,3,4], [3,5,4], [2,7,2], [1,3,2]])
M2 = np.array([[2,3,3], [3,2,7], [3,4,2], [3,2,1]])


S1 = np.matmul(M1,M1.T)
S2 = np.matmul(M2,M2.T)

print('\n\nS1\n', S1)
print('\n\nS2\n', S2)

# Adding S1 and S2
print('\n\nS1 + S2\n', S1+S2)

Output:

S1
 [[29 37 33 19]
 [37 50 49 26]
 [33 49 57 27]
 [19 26 27 14]]


S2
 [[22 33 24 15]
 [33 62 31 20]
 [24 31 29 19]
 [15 20 19 14]]


S1 + S2
 [[ 51  70  57  34]
 [ 70 112  80  46]
 [ 57  80  86  46]
 [ 34  46  46  28]]