C Program to find the trace and normal of a matrix

For a better understanding, we always recommend you to learn the basic topics of C programming listed below:

In this c program, we need to calculate the trace and normal of a matrix. A matrix is a collection of elements of the same data type, which we arrange in a 2d format. A matrix is also called an array of arrays.

How to calculate the trace of a matrix?

Trace is the Sum of all elements of the Main diagonal of a Matrix. For example, The Trace of Matrix A :

2 5
2
1 is 3.

How to calculate the normal of a matrix?

The normal of a matrix is the square root of the Sum of squares of the elements of Matrix. For example, The Normal of Matrix B:

2 10
8  5
is 5. That is the Square root of 25.

So here in this c program, what we are doing is to initialize the variables and import the header files. Then accept a matrix using a nested for loop and calculate the square of each element. Now add the product to a sum variable. Find out the normal by calculating the square root of the sum.

For finding a trace of that matrix, we initiate a for loop where we add the elements of the main diagonal of the matrix. Then we display the normal and the trace of the matrix using the printf function. 

ALGORITHM

STEP 1: Include the Header files to use the built-in functions in the C program.

STEP 2: Include the Header file math.h.

STEP 3: Declare the variable i, j, m, n, sum, sum1, a, normal and set sum=0, sum1=0, a=0.

STEP 4: Read the order of the Matrix into the variables m and n.

STEP 5: Read the coefficients of the matrix into the array ma[i][j] and calculate a=ma[i][j]*ma[i][j] ,sum1=sum1+a using nested for loop.

STEP 6: Calculate Normal=sqrt(sum1).

STEP 7: Display the normal of the given Matrix is normal.

STEP 8: By using the for loop with the condition i

STEP 9: Display the Trace of the Matrix as a sum.

C Source Code

                                          #include <stdio.h>
#include <math.h>

void main() {
  static int ma[10][10];
  int i, j, m, n, sum = 0, sum1 = 0, a = 0, normal;
  printf("Enter the order of the matrix\n");
  scanf("%d %d", & m, & n);
  printf("Enter the no coefficients of the matrix \n");
  for (i = 0; i < m; ++i) {
    for (j = 0; j < n; ++j) {
      scanf("%d", & ma[i][j]);
      a = ma[i][j] * ma[i][j];
      sum1 = sum1 + a;
    }
  }
  normal = sqrt(sum1);
  printf("The normal of the given matrix is = %d\n", normal);
  for (i = 0; i < m; ++i) {
    sum = sum + ma[i][i];
  }
  printf("Trace of the matrix is = %d\n", sum);
} /*End of main() */
                                      

OUTPUT

Enter the order of the matrix
3*3

Enter the n coefficients of the matrix
1 2 3
4 5 6
7 8 9

The normal of the given matrix is = 16
Trace of the matrix is = 15

Run 2

Enter the order of the matrix
2*2

Enter the n coefficients of the matrix
2 4
6 8

The normal of the given matrix is = 10

Trace of the matrix                       = 10