Trace of matrix

In this example we will find the Trace of matrix

#include <iostream>

using namespace std;

const int MAX = 100;

int FindTrace(int arr[][MAX], int n){
    int sum = 0;
    for(int i = 0; i < n; i++){
            sum += arr[i][i];
        }
    return sum;
}

int main(){
    int arr[][MAX] = {{2,5,8,4},
                      {3,5,8,4},
                      {8,4,9,5},
                      {4,9,6,2}};

    cout<<"Trace of Matrix: "<<FindTrace(arr,4)<<endl;
    return 0;
}

Output:

Trace of Matrix: 18

Explanation:

Step1: Constants and Function Declaration

const int MAX = 100;

This defines a constant MAX which sets the maximum size of the matrix (100). It is used as the upper limit for the number of columns in the matrix.

Step2 : FindTrace Function

int FindTrace(int arr[][MAX], int n){
    int sum = 0;
    for(int i = 0; i < n; i++){
        sum += arr[i][i];
    }
    return sum;
}

This function computes the trace of the matrix. It takes two parameters:

• arr[][MAX]: A 2D array (matrix) of integers where the second dimension is limited by MAX.
• n: The size of the matrix (i.e., number of rows or columns since it’s a square matrix).

Within the function:

• It initializes sum to 0.
• Then it loops over the diagonal elements of the matrix (elements where i == j), adding them to sum.
• Finally, it returns the calculated sum.

Step3: Main Function

int main(){
    int arr[][MAX] = {{2,5,8,4},
                      {3,5,8,4},
                      {8,4,9,5},
                      {4,9,6,2}};
    cout<<"Trace of Matrix: "<<FindTrace(arr,4)<<endl;
    return 0;
}

In the main() function:

• A 4×4 matrix arr is declared and initialized with specific values.
• The function FindTrace(arr, 4) is called, passing the matrix and its size (4) as arguments.
• The trace of the matrix is calculated and printed to the console.