C Program for Matrix Multiplication

C Program to Multiply Two Matrices

To multiply two matrices in C, you must first understand the basics of matrix operations. A matrix is essentially a rectangular array of numbers arranged in rows & columns. For multiplication, the number of columns in the first matrix must match the number of rows in the second matrix.

Here’s a simple C program to demonstrate matrix multiplication:

• C

C

#include <stdio.h>

int main() {
    int a[10][10], b[10][10], result[10][10], r1, c1, r2, c2, i, j, k;

    printf("Enter rows & columns for the first matrix: ");
    scanf("%d %d", &r1, &c1);
    printf("Enter rows & columns for the second matrix: ");
    scanf("%d %d", &r2, &c2);

    // Checking if multiplication is possible
    if (c1 != r2) {
        printf("Matrix multiplication not possible.\n");
        return 0;
    }

    // Taking input for the first matrix
    printf("Enter elements of matrix 1:\n");
    for (i = 0; i < r1; i++)
        for (j = 0; j < c1; j++)
            scanf("%d", &a[i][j]);

    // Taking input for the second matrix
    printf("Enter elements of matrix 2:\n");
    for (i = 0; i < r2; i++)
        for (j = 0; j < c2; j++)
            scanf("%d", &b[i][j]);

    // Initializing elements of result matrix to 0
    for (i = 0; i < r1; i++)
        for (j = 0; j < c2; j++)
            result[i][j] = 0;

    // Multiplying matrices a & b & storing in result
    for (i = 0; i < r1; i++) {
        for (j = 0; j < c2; j++) {
            for (k = 0; k < c1; k++) {
                result[i][j] += a[i][k] * b[k][j];
            }
        }
    }

    // Displaying the result
    printf("Output Matrix:\n");
    for (i = 0; i < r1; i++) {
        for (j = 0; j < c2; j++)
            printf("%d  ", result[i][j]);
        printf("\n");
    }

    return 0;
}

You can also try this code with Online C Compiler

Run Code

Output

This program first checks if the multiplication is feasible by matching the columns of the first matrix with the rows of the second. It then takes user inputs for both matrices, performs the multiplication, & displays the resulting matrix.

Complexity Analysis of Matrix Multiplication in C

When we multiply matrices, it's important to understand how much computational work is being done. This is often described in terms of complexity. For matrix multiplication, the complexity mainly depends on the number of rows and columns in the matrices.

Assuming you are multiplying two matrices, A and B, where A is of size m x n and B is n x p, the resultant matrix C will be of size m x p. To compute each element in C, we perform n multiplications and n-1 additions. This calculation needs to be done for every element of the resulting matrix.

Here's a simple breakdown:
 

• For each of the m rows in matrix A, and for each of the p columns in matrix B, the innermost loop runs n times.
   
• Therefore, the total number of operations (both multiplications and additions) is approximately m * n * p.

In terms of big O notation, we describe this complexity as O(mnp). This means the time to compute the matrix multiplication increases linearly with the number of operations required, which is a direct product of the dimensions of the involved matrices.

Frequently Asked Questions

What happens if the matrices are not compatible for multiplication?

If the number of columns in the first matrix does not match the number of rows in the second matrix, multiplication cannot proceed. In C, this will typically not result in a compiler error but may cause runtime errors or incorrect results. Always check the dimensions of your matrices before attempting to multiply them to ensure they are compatible.

Can matrix multiplication be done in place?

In matrix multiplication, the result matrix is usually separate because the dimensions of the result might not match either of the original matrices. Moreover, trying to use one of the original matrices to store the result can overwrite data that is still needed for calculations, leading to incorrect results.

How can I optimize matrix multiplication for better performance?

To optimize matrix multiplication, consider using more advanced algorithms like Strassen's algorithm, which reduces the complexity from O(n^3) to approximately O(n^2.81). Additionally, optimizing memory access patterns and using parallel processing techniques, such as multithreading or employing GPU computations, can significantly speed up the multiplication process, especially for large matrices.

What is the fastest algorithm for matrix multiplication?

The fastest matrix multiplication algorithm is a variant of the Coppersmith-Winograd algorithm, with an improved time complexity of O(n^{2.3728596}), achieved by Le Gall. While theoretically faster, these advanced algorithms are complex and less practical for implementation compared to simpler methods like Strassen's algorithm for most applications.

Conclusion

In this article, we have learned how to multiply two matrices using C programming. We started by setting up the development environment necessary for compiling and running C programs. Then, we moved on to discussing how to declare and initialize matrices in C, followed by a detailed explanation of the multiplication process using nested loops. We also discussed the complexity analysis of matrix multiplication, helping you understand the computational effort involved. 

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