Python Program to Calculate the Trace of a Matrix

Introduction

The trace of a matrix is the sum of the elements on its main diagonal (the diagonal that runs from the top-left corner to the bottom-right corner). This operation is only defined for square matrices (matrices with the same number of rows and columns). The trace is often used in linear algebra for various applications. This tutorial will guide you through creating a Python program that calculates the trace of a matrix.

Example:

Matrix:
```
1 2 3
4 5 6
7 8 9
```
Trace: 1 + 5 + 9 = 15

Problem Statement

Create a Python program that:

Takes a square matrix as input.
Calculates the trace of the matrix (sum of the main diagonal elements).
Displays the trace of the matrix.

Solution Steps

Take Matrix Dimensions: Ask the user for the number of rows and columns.
Initialize the Matrix: Create an empty matrix to store the input values.
Input Matrix Elements: Use nested loops to take input for each element of the matrix.
Check for Square Matrix: Ensure the matrix is square (number of rows equals number of columns).
Calculate the Trace: Sum the elements on the main diagonal of the matrix.
Display the Trace: Print the resulting trace.

Python Program

# Python Program to Calculate the Trace of a Matrix
# Author: https://www.rameshfadatare.com/

# Step 1: Take the number of rows and columns as input
rows = int(input("Enter the number of rows (and columns, since it's a square matrix): "))
columns = rows  # For a square matrix, rows and columns are equal

# Step 2: Initialize the matrix
matrix = []

# Step 3: Input matrix elements
print("Enter the elements of the matrix:")
for i in range(rows):
    row = []
    for j in range(columns):
        element = int(input(f"Element at position ({i+1}, {j+1}): "))
        row.append(element)
    matrix.append(row)

# Step 4: Calculate the trace of the matrix
trace = 0
for i in range(rows):
    trace += matrix[i][i]

# Step 5: Display the trace
print("\nThe trace of the matrix is:", trace)

Explanation

Step 1: Take the Number of Rows and Columns as Input

The input() function is used to take the number of rows from the user. Since the matrix is square, the number of columns is set equal to the number of rows.

Step 2: Initialize the Matrix

An empty list matrix is initialized to store the elements of the matrix.

Step 3: Input Matrix Elements

A nested loop is used to take input for each element of the matrix. Each element is appended to the corresponding row, and the row is then appended to matrix.

Step 4: Calculate the Trace of the Matrix

The trace is calculated by summing the elements on the main diagonal. The main diagonal elements are those where the row index equals the column index (i.e., matrix[i][i]).

Step 5: Display the Trace

The trace is displayed using the print() function.

Output Example

Example Output:

Enter the number of rows (and columns, since it's a square matrix): 3
Enter the elements of the matrix:
Element at position (1, 1): 1
Element at position (1, 2): 2
Element at position (1, 3): 3
Element at position (2, 1): 4
Element at position (2, 2): 5
Element at position (2, 3): 6
Element at position (3, 1): 7
Element at position (3, 2): 8
Element at position (3, 3): 9

The trace of the matrix is: 15

Additional Examples

Example 1: Trace of a 2×2 Matrix

# Example of a 2x2 matrix
rows = 2
columns = 2
matrix = [
    [4, 5],
    [6, 7]
]

# Calculating the trace
trace = 0
for i in range(rows):
    trace += matrix[i][i]

# Displaying the trace
print("\nThe trace of the 2x2 matrix is:", trace)

Output:

The trace of the 2x2 matrix is: 11

Example 2: Trace of a 4×4 Matrix

# Example of a 4x4 matrix
rows = 4
columns = 4
matrix = [
    [10, 20, 30, 40],
    [50, 60, 70, 80],
    [90, 100, 110, 120],
    [130, 140, 150, 160]
]

# Calculating the trace
trace = 0
for i in range(rows):
    trace += matrix[i][i]

# Displaying the trace
print("\nThe trace of the 4x4 matrix is:", trace)