# Python Program to Transpose a Matrix

In this example, you will learn to transpose a matrix (which is created by using a nested list).

To understand this example, you should have the knowledge of the following Python programming topics:

In Python, we can implement a matrix as a nested list (list inside a list). We can treat each element as a row of the matrix.

For example X = [[1, 2], [4, 5], [3, 6]] would represent a 3×2 matrix. The first row can be selected as X. And, the element in the first-row first column can be selected as X.

Transpose of a matrix is the interchanging of rows and columns. It is denoted as X’. The element at ith row and jth column in X will be placed at jth row and ith column in X’. So if X is a 3×2 matrix, X’ will be a 2×3 matrix.

Here are a couple of ways to accomplish this in Python.

## 1. Matrix Transpose using Nested Loop

# Program to transpose a matrix using a nested loop

X = [[12,7],
[4 ,5],
[3 ,8]]

result = [[0,0,0],
[0,0,0]]

# iterate through rows
for i in range(len(X)):
# iterate through columns
for j in range(len(X)):
result[j][i] = X[i][j]

for r in result:
print(r)


Output

[12, 4, 3]
[7, 5, 8]


In this program, we have used nested for loops to iterate through each row and each column. At each point we place the X[i][j] element into result[j][i].

## 2. Matrix Transpose using Nested List Comprehension

''' Program to transpose a matrix using list comprehension'''

X = [[12,7],
[4 ,5],
[3 ,8]]

result = [[X[j][i] for j in range(len(X))] for i in range(len(X))]

for r in result:
print(r)


The output of this program is the same as above. We have used nested list comprehension to iterate through each element in the matrix.