Lesson 3

Transposing Matrices in Python

Introduction

Hello there! Are you ready to hone your Python programming skills with another exciting exercise? In this unit, we are plunging into the world of matrices. More specifically, we'll be transposing a given matrix. Let's dive into this matrix manipulation game without delay!

Task Statement

To begin, let's elaborate on the task at hand. You are required to write a Python function named transformMatrix(). This function will accept a 2D list (which represents a matrix) that contains integers as inputs. Your responsibility is to return another 2D list, which is the transposed version of the given matrix.

Remember, when we mention 'transposing a matrix', we are referring to the process of switching its rows and columns. In other words, all the rows of the original matrix should convert into columns in the transposed matrix, and vice versa.

For instance, if the original matrix (input 2D list) is:

Python
1[ 2 [1, 2, 3], 3 [4, 5, 6] 4]

Then the transposed matrix (output 2D list) will be:

Python
1[ 2 [1, 4], 3 [2, 5], 4 [3, 6] 5]

Let me remind you that it is vital for your result to maintain the integrity of the data type that is present in the original matrix. In layman's terms, the values seen in the input matrix are integers, and they should be integers in the output matrix as well.

Solution Building: Step 1

The initial step of building our solution involves determining the dimensions of the matrix. We need to know the number of rows and columns present in it. The Python len() function can offer this information. The number of rows is simply the length of the matrix (the outer list), and the number of columns matches the length of any of the inner lists.

Python
1def transformMatrix(matrix): 2 rows = len(matrix) 3 cols = len(matrix[0]) if rows > 0 else 0
Solution Building: Step 2

The subsequent step is to create a "placeholder" for the transposed matrix that is in alignment with its required dimensions. This will be a new 2D list, but with the number of rows and columns swapped. Initially, we can populate this matrix with all zeros.

Python
1def transformMatrix(matrix): 2 rows = len(matrix) 3 cols = len(matrix[0]) if rows > 0 else 0 4 result = [[0 for _ in range(rows)] for _ in range(cols)]
Solution Building: Step 3

It's time to get to the crux of the matter - transposing the matrix. For every element in the original matrix, we want to move it from the ith row and jth column to the jth row and ith column of the transposed matrix. A straightforward nested for-loop can effortlessly execute this swap for all elements of the matrix.

Python
1def transformMatrix(matrix): 2 rows = len(matrix) 3 cols = len(matrix[0]) if rows > 0 else 0 4 result = [[0 for _ in range(rows)] for _ in range(cols)] 5 6 for i in range(rows): 7 for j in range(cols): 8 result[j][i] = matrix[i][j] 9 10 return result 11 12# Initial matrix (2D list) 13matrix = [ 14 [1, 2, 3], 15 [4, 5, 6] 16] 17 18# Call our function on the matrix and output the result 19transposed = transformMatrix(matrix) 20print(transposed) # Outputs: [[1, 4], [2, 5], [3, 6]]

This step concludes our solution!

Alternative Solution

Another solution could be written by using only the short array creation syntax:

Python
1def transformMatrix(matrix): 2 rows = len(matrix) 3 cols = len(matrix[0]) if rows > 0 else 0 4 result = [[matrix[j][i] for j in range(rows)] for i in range(cols)] 5 6 return result

Here we fill the matrix directly at the creation, and the j-th column of the i-th row of the new matrix is assigned the value matrix[j][i].

Lesson Summary

With this, we've brought this lesson to a close! Congratulations on successfully implementing a function that can transpose matrices! This task is not simple, but by accomplishing it, you've exhibited your understanding of and proficiency in Python's lists, for-loops, and the concept of matrix transposition.

Your hard work continues though. Now that you have acquired this valuable skill, it's time to reinforce it with more practice. During the next session, you will encounter practice problems that build on this concept. So, get ready and start coding!

Enjoy this lesson? Now it's time to practice with Cosmo!

Practice is how you turn knowledge into actual skills.