Python Program to Transpose a Matrix

The transpose of a matrix is a new matrix that is obtained by interchanging its rows and columns. The transpose of a matrix is denoted by placing a superscript “T” after the original matrix name.

For example, consider the following matrix A:

A = 
[
  1 2 3
  4 5 6
  7 8 9
]

The transpose of matrix A is denoted by A^T and is obtained by interchanging its rows and columns, resulting in:

A^T = 
[
  1 4 7
  2 5 8
  3 6 9
]

The transpose of a matrix can be useful in various ways. For example, it can be used to find the dot product of two matrices, or to convert a row vector into a column vector, or vice versa. It is also used in the process of solving systems of linear equations and in other areas of mathematics and engineering.

Python Code : #

The below Python program to transpose a matrix:

# Define a matrix A
A = [[1, 2, 3],
     [4, 5, 6],
     [7, 8, 9]]

# Create a matrix to hold the transpose of A
transpose = [[0, 0, 0],
             [0, 0, 0],
             [0, 0, 0]]

# Transpose the matrix A and store the result in transpose
for i in range(len(A)):
    for j in range(len(A[0])):
        transpose[j][i] = A[i][j]

# Display the resulting transposed matrix
for row in transpose:
    print(row)

Explanation:

1. The matrix A is defined as a 3x3 list of lists.

2. A matrix transpose is created as a 3x3 list of lists initialized to all zeros.

3. The matrix A is transposed by iterating over its rows and columns using a nested for loop. The element at position (i, j) in the original matrix A is moved to position (j, i) in the transposed matrix.

4. The resulting transposed matrix is displayed using a for loop that iterates over the rows of the matrix and prints each row.

For Example:

[1, 4, 7]
[2, 5, 8]
[3, 6, 9]