C Program To Find Normal and Trace of Matrix

Here, we will see how to write a C program to find the normal and trace of a matrix. Below are the examples:

Input: mat[][] = {{1, 2, 3},
                           {4, 5, 6},
                           {7, 8, 9}};
Output:

• Normal = 16
• Trace  = 15

Explanation:

• Normal = sqrt(1*1+ 2*2 + 3*3 + 4*4 + 5*5 + 6*6 + 7*7 + 8*8 + 9*9) = 16
• Trace  = 1+5+9 = 15

Input: mat[][] = {{5, 6, 1},
                          {7, 2, 9},
                          {6, 1, 3}};
Output:

• Normal = 10
• Trace  = 10

Explanation:

• Normal = sqrt(5*5+ 6*6 + 1*1 + 7*7 + 2*2 + 9*9 + 6*6 + 1*1 + 3*3) = 15
• Trace  = 5+2+3 = 10

For a better understanding see the below image.

Approach:

1. To Find Normal:

• Run nested loop to access elements of the matrix.
• Find the sum of all the elements present in the matrix.
• Then return the square root of that sum.

2. To Find Trace:

• Run a single loop to access diagonal elements of the matrix.
• Return the sum of diagonal elements.

Below is the C program to find normal and the trace of a matrix:

C

// C program to find trace
// and normal of given matrix
#include <math.h>
#include <stdio.h>

// Returns Normal of a matrix
// of size n x n
int findNormal(int mat[][3],
               int n)
{
    int sum = 0;

    // Run nested loop to access
    // elements of matrix
    for (int i = 0; i < n; i++)
        for (int j = 0; j < n; j++)
            sum += mat[i][j] * mat[i][j];
    return sqrt(sum);
}

// Returns trace of a matrix of
// size n x n
int findTrace(int mat[][3], int n)
{
    int sum = 0;

    // Run a loop to access diagonal
    // elements of matrix
    for (int i = 0; i < n; i++)
        sum += mat[i][i];
    return sum;
}

// Driven code
int main()
{
    int mat[3][3] = {{1, 2, 3},
                     {4, 5, 6},
                     {7, 8, 9}};
    printf("Normal of Matrix = %d",
            findNormal(mat, 3));
    printf("\nTrace of Matrix = %d",
            findTrace(mat, 3));
    return 0;
}

Output

Normal of Matrix = 16
Trace of Matrix = 15

Time Complexity: O(n*n) 
Space Complexity: O(1)