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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.
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
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)
[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.