A Python program to display the transpose of a matrix.

 

The transpose of a matrix is obtained by interchanging its rows and columns. If a matrix A has dimensions n x m, then its transpose, denoted by A^T, has dimensions m x n.

For example, consider the following 2x3 matrix A:

Python
[ 1  2  3 ]
[ 4  5  6 ]

The transpose of A, denoted by A^T, is obtained by interchanging its rows and columns, as follows:

Python
[ 1  4 ]
[ 2  5 ]
[ 3  6 ]

As we can see, the rows of the original matrix become the columns of the transpose, and the columns of the original matrix become the rows of the transpose. The transpose of a matrix is obtained by reflecting the matrix along its main diagonal.

The transpose of a matrix has several useful properties, such as being distributive over addition and subtraction, and preserving the dot product of vectors. It is also used in many applications, including linear algebra, signal processing, and control theory, among others.

Here's a Python program to display the transpose of a matrix, both before and after the transposition:

Python
# Function to display a matrix
def display_matrix(matrix):
    for row in matrix:
        print(row)

# Function to transpose a matrix
def transpose(matrix):
    n = len(matrix)
    m = len(matrix[0])
    transposed_matrix = [[matrix[j][i] for j in range(n)] for i in range(m)]
    return transposed_matrix

# Get matrix from user input
n = int(input("Enter number of rows: "))
m = int(input("Enter number of columns: "))
matrix = []
for i in range(n):
    row = list(map(int, input(f"Enter elements of row {i+1}: ").split()))
    matrix.append(row)

# Display matrix before transposition
print("Matrix before transposition:")
display_matrix(matrix)

# Transpose matrix
transposed_matrix = transpose(matrix)

# Display matrix after transposition
print("Matrix after transposition:")
display_matrix(transposed_matrix)

In this program, the user is prompted to enter the number of rows and columns in the matrix, and then to enter the elements of each row. The program then calls the display_matrix function to display the matrix before transposition, transposes the matrix using the transpose function, and displays the matrix after transposition.

Here's an example input and output of the program:

Python
Enter number of rows: 3
Enter number of columns: 2
Enter elements of row 1: 1 2
Enter elements of row 2: 3 4
Enter elements of row 3: 5 6
Matrix before transposition:
[1, 2]
[3, 4]
[5, 6]
Matrix after transposition:
[1, 3, 5]
[2, 4, 6]

Note that the transpose of a matrix is obtained by interchanging its rows and columns. If the original matrix has dimensions n x m, then its transpose has dimensions m x n. Also, the transpose of a matrix is obtained by reflecting the matrix along its main diagonal.