Matrix Addition

Yaser Rahmati | یاسر رحمتی

Definition

Matrix addition is a fundamental operation in linear algebra, commonly used in various mathematical and computational contexts. Adding two matrices together involves adding their corresponding elements.

Condition

Two matrices can be added together only if they have the same dimensions, meaning they have the same number of rows and the same number of columns.

Example

Suppose we have two matrices A and B:

$$A=\begin{bmatrix} 1 & 2\\ 3 & 4 \end{bmatrix} , B=\begin{bmatrix} 5 & 6\\ 7 & 8 \end{bmatrix}$$

Step 1

First, identify the dimensions of the matrices. In this example, both matrices A and B have 2 rows and 2 columns.

Step 2

To add these two matrices together, we simply add the corresponding elements in the matrices to form a new matrix.

$$A+B=\begin{bmatrix} (1+5) & (2+6)\\ (3+7) & (4+8) \end{bmatrix} = \begin{bmatrix} 6 & 8\\ 10 & 12 \end{bmatrix}$$

Python

import numpy as np

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

# Add the matrices using NumPy's addition operator
result = np.add(matrix1, matrix2)

# Print the resulting matrix
print(result)

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