Transpose a Matrix

In Python, we can implement a matrix as 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. First row can be selected as X[0] and the element in 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

Source Code

# Program to transpose a matrix using 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[0])):
       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].

Matrix Transpose using Nested List Comprehension

Source Code

# 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:
   print(r)

Explanation

The output of this program is the same as above. We have used nested list comprehension to iterate through each element in the matrix. List comprehension allows us to write concise codes and we must try to use them frequently in Python. They are very helpful.