C Program To Find Normal and Trace of Matrix

Last Updated : 04 Jul, 2022

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)

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