Python Program to Transpose a Matrix

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 3x2 matrix. The first row can be selected as X[0]. And, the element in the first-row first column can be selected as X[0][0].

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 3x2 matrix, X' will be a 2x3 matrix.

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

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],

# iterate through rows
for i in range(len(X)):
   # iterate through columns
   for j in range(len(X[0])):
       result[j][i] = X[i][j]

for r in result:


[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].

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[0]))]

for r in result:

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

To learn more, visit Python List Comprehension.

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