Example: Calculate Trace and Frobenius Normal of a Matrix in C

// Calculate Trace and Frobenius Normal of a Matrix
#include <stdio.h>
#include <math.h> // Required for sqrt and pow functions

#define MAX_SIZE 10 // Maximum size for matrix

// Function to calculate the trace of a square matrix
double calculateTrace(int matrix[MAX_SIZE][MAX_SIZE], int size) {
    double trace = 0.0;
    for (int i = 0; i < size; i++) {
        trace += matrix[i][i]; // Sum main diagonal elements
    }
    return trace;
}

// Function to calculate the Frobenius normal of a matrix
double calculateFrobeniusNormal(int matrix[MAX_SIZE][MAX_SIZE], int rows, int cols) {
    double sumOfSquares = 0.0;
    for (int i = 0; i < rows; i++) {
        for (int j = 0; j < cols; j++) {
            sumOfSquares += pow(matrix[i][j], 2); // Add square of each element
        }
    }
    return sqrt(sumOfSquares); // Return square root of the sum
}

int main() {
    int size;
    int matrix[MAX_SIZE][MAX_SIZE];

    // Step 1: Get matrix size from the user
    printf("Enter the size of the square matrix (e.g., 3 for 3x3): ");
    scanf("%d", &size);

    if (size <= 0 || size > MAX_SIZE) {
        printf("Invalid size. Please enter a size between 1 and %d.\n", MAX_SIZE);
        return 1; // Indicate an error
    }

    // Step 2: Get matrix elements from the user
    printf("Enter the elements of the matrix row by row:\n");
    for (int i = 0; i < size; i++) {
        for (int j = 0; j < size; j++) {
            printf("Enter element [%d][%d]: ", i, j);
            scanf("%d", &matrix[i][j]);
        }
    }

    // Step 3: Print the entered matrix (optional)
    printf("\nEntered Matrix:\n");
    for (int i = 0; i < size; i++) {
        for (int j = 0; j < size; j++) {
            printf("%4d ", matrix[i][j]);
        }
        printf("\n");
    }

    // Step 4: Calculate and print the trace
    double trace = calculateTrace(matrix, size);
    printf("\nTrace of the matrix: %.2f\n", trace);

    // Step 5: Calculate and print the Frobenius Normal
    // For a square matrix, rows and cols are the same as 'size'
    double normal = calculateFrobeniusNormal(matrix, size, size);
    printf("Frobenius Normal of the matrix: %.2f\n", normal);

    return 0;
}