# 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:

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

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

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.

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]
```