To understand this example, you should have the knowledge of following Python programming topics:
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.
X = [[1, 2], [4, 5], [3, 6]] would represent a 3x2 matrix. First row can be selected as
X and the element in 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 3x2 matrix, X' will be a 2x3 matrix.
Here are a couple of ways to accomplish this in Python.
# 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)): 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].
''' 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.
List comprehension allows us to write concise codes and we must try to use them frequently in Python. They are very helpful.