Matrix addition and subtraction are fundamental operations in linear algebra, allowing for the direct combination or comparison of matrix elements. These operations are critical in various computational tasks, such as combining data, adjusting measurements, or calculating differences.

Performing Matrix Addition

To add two matrices, they must be of the same size, meaning they must have the same number of rows and columns. Here’s how you can perform matrix addition using the np.add() function: 

import numpy as np

# Define two matrices
matrix1 = np.array([[1, 2],
                    [3, 4]])
matrix2 = np.array([[5, 6],
                    [7, 8]])

# Perform matrix addition
addition_result = np.add(matrix1, matrix2)

print("Result of Matrix Addition:\n", addition_result)

Output:

Result of Matrix Addition:
[[ 6  8]
 [10 12]]

Performing Matrix Subtraction

Similar to addition, matrix subtraction requires that both matrices have the same dimensions. Here’s how to subtract one matrix from another using the np.subtract() function: 

import numpy as np

# Define two matrices
matrix1 = np.array([[5, 6],
                    [7, 8]])
matrix2 = np.array([[1, 2],
                    [3, 4]])

# Perform matrix subtraction
subtraction_result = np.subtract(matrix1, matrix2)

print("Result of Matrix Subtraction:\n", subtraction_result)

Output:

Result of Matrix Subtraction:
[[ 4  4]
 [ 4  4]]

Handling Dimension Mismatch

If you attempt to add or subtract matrices of different dimensions, NumPy will raise an error indicating the shapes are not aligned. Here’s what happens when trying to add two matrices of different sizes:

import numpy as np

# Define matrices of different sizes
matrix1 = np.array([[1, 2],
                    [3, 4]])
matrix2 = np.array([[5, 6, 7],
                    [8, 9, 10]])

# Attempt to perform matrix addition
try:
    addition_result = np.add(matrix1, matrix2)
except ValueError as e:
    print("Error:", e)

Output:

Error: operands could not be broadcast together with shapes (2,2) (2,3)

Matrix addition and subtraction are straightforward yet powerful tools in matrix algebra. These operations form the basis for more complex algebraic manipulations and are integral to many types of data analysis and scientific computing tasks. For instance, in image processing, these operations can be used to blend images or remove noise. This guide provides a practical introduction to adding and subtracting matrices in Python, ensuring you can apply these techniques to your projects.