Matrix Multiplication in C
A matrix is a collection of numbers organized in rows and columns. Matrices can be manipulated using operations like Addition, Subtraction, and Multiplication. Multiplying two matrices is only possible when the number of columns in the first matrix matches the number of rows in the second matrix.
The result of two matrix multiplication in C is obtained by calculating the dot product of each row of the first matrix with each column of the second matrix.
To better understand this article, it is recommended that you have prior knowledge of the following C Programming topics:
Today, we will be covering the following sections:
- Introduction to Matrix Multiplication
- Matrix Multiplication in C
- Matrix Multiplication by Passing it to a Function in C
Introduction to Matrix Multiplication
Matrix multiplication is a fundamental operation in linear algebra, used in many applications such as computer graphics, physics, economics, and engineering. It involves multiplying two matrices to obtain a new matrix that represents the composition of the two original matrices.
To perform matrix multiplication, we need to follow a specific rule: the number of columns in the first matrix must be equal to the number of rows in the second matrix. If this condition is met, the resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.
The process of matrix multiplication involves multiplying each element of a row in the first matrix with the corresponding element in a column of the second matrix, and then adding the products together. This operation is repeated for every row and column pair until all elements in the resulting matrix are computed.
Matrix multiplication is not commutative, which means that the order of the matrices matters. In other words, multiplying matrix A by matrix B may produce a different result than multiplying matrix B by matrix A.
We recommend you to check out this Beginner’s Guide to Understand and Implement Matrix Multiplication to have a more thorough knowledge of this topic.
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Matrix Multiplication in C
There are mainly two types of matrices:
- Square matrix
- Rectangle matrix
Let’s look at the multiplication of both of these matrices in C:
Square Matrix Multiplication in C
A square matrix is defined as a matrix with the same number of rows and columns. The multiplication of two square matrices of the same order is only possible if both matrices have the same order.
To compute the product of two matrices, we multiply the corresponding elements of the matrices and sum up the products. Let us see how this is achieved using C programming:
#include <stdio.h> #define N 3 // Size of square matrices int main() { int matrix1[N][N] = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}; int matrix2[N][N] = {{9, 8, 7}, {6, 5, 4}, {3, 2, 1}}; int result[N][N]; int i, j, k; // Multiply the two matrices for (i = 0; i < N; i++) { for (j = 0; j < N; j++) { int sum = 0; for (k = 0; k < N; k++) { sum += matrix1[i][k] * matrix2[k][j]; } result[i][j] = sum; } } // Print the resulting matrix printf("Result Matrix:\n"); for (i = 0; i < N; i++) { for (j = 0; j < N; j++) { printf("%d ", result[i][j]); } printf("\n"); } return 0; }
Output:
In this example, we have two 3×3 square matrices: matrix1 and matrix2. We declare a new matrix result to store the result of the multiplication.
We then use three nested loops to multiply the two matrices: the outermost loop iterates over the rows of the first matrix, the middle loop iterates over the columns of the second matrix, and the innermost loop iterates over the elements in the rows and columns.
The product of each corresponding element in the row of the first matrix and column of the second matrix is calculated and summed up to obtain the resulting element in the result matrix.
Finally, we print the resulting matrix to the console.
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Rectangle Matrix Multiplication in C
A rectangular matrix is a matrix that has a different number of rows and columns.
The rules for determining if two rectangular matrices can be multiplied remain the same as those for square matrices. Specifically, the number of columns in the first matrix must be equal to the number of rows in the second matrix.
Below is a code example that demonstrates how to find the product of two rectangular matrices:
#include <stdio.h> #define ROWS_A 2 #define COLS_A 3 #define ROWS_B 3 #define COLS_B 4 int main() { int matrix_a[ROWS_A][COLS_A] = {{1, 2, 3}, {4, 5, 6}}; int matrix_b[ROWS_B][COLS_B] = {{7, 8, 9, 10}, {11, 12, 13, 14}, {15, 16, 17, 18}}; int result[ROWS_A][COLS_B]; int i, j, k; // Multiply the two matrices for (i = 0; i < ROWS_A; i++) { for (j = 0; j < COLS_B; j++) { int sum = 0; for (k = 0; k < ROWS_B; k++) { sum += matrix_a[i][k] * matrix_b[k][j]; } result[i][j] = sum; } } // Print the resulting matrix printf("Result Matrix:\n"); for (i = 0; i < ROWS_A; i++) { for (j = 0; j < COLS_B; j++) { printf("%d ", result[i][j]); } printf("\n"); } return 0; }
Output:
In this example, we have two rectangular matrices: matrix_a, which is a 2×3 matrix, and matrix_b, which is a 3×4 matrix. We declare a new matrix result to store the result of the multiplication.
We then use three nested loops to multiply the two matrices: the outermost loop iterates over the rows of the first matrix, the middle loop iterates over the columns of the second matrix, and the innermost loop iterates over the elements in the rows and columns.
The product of each corresponding element in the row of the first matrix and column of the second matrix is calculated and summed up to obtain the resulting element in the result matrix.
Finally, we print the resulting matrix to the console.
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Matrix Multiplication by Passing it to a Function in C
In C, you can also multiply matrices by passing them to a function. Here’s an example of multiplying two matrices by passing them to a function in C:
#include <stdio.h> #define ROWS_A 2 #define COLS_A 3 #define ROWS_B 3 #define COLS_B 4 void multiply_matrices(int matrix_a[][COLS_A], int matrix_b[][COLS_B], int result[][COLS_B], int rows_a, int cols_a, int cols_b) { int i, j, k; // Multiply the two matrices for (i = 0; i < rows_a; i++) { for (j = 0; j < cols_b; j++) { int sum = 0; for (k = 0; k < ROWS_B; k++) { sum += matrix_a[i][k] * matrix_b[k][j]; } result[i][j] = sum; } } } int main() { int matrix_a[ROWS_A][COLS_A] = {{1, 2, 3}, {4, 5, 6}}; int matrix_b[ROWS_B][COLS_B] = {{7, 8, 9, 10}, {11, 12, 13, 14}, {15, 16, 17, 18}}; int result[ROWS_A][COLS_B]; // Multiply the matrices by passing them to a function multiply_matrices(matrix_a, matrix_b, result, ROWS_A, COLS_A, COLS_B); // Print the resulting matrix printf("Result Matrix:\n"); for (int i = 0; i < ROWS_A; i++) { for (int j = 0; j < COLS_B; j++) { printf("%d ", result[i][j]); } printf("\n"); } return 0; }
In this example, we define a function multiply_matrices that takes in two matrices (matrix_a and matrix_b). As well as their dimensions (rows_a, cols_a, and cols_b) and a matrix to store the result (result). Inside the function, we use the same nested loops as before to perform the matrix multiplication and store the result in result.
In the main function, we declare the matrices matrix_a, matrix_b, and result, and pass them to the multiply_matrices function along with their dimensions.
The resulting matrix is then printed to the console using the same loop structure as before.
The output of this code will be the same as before:
This approach allows you to reuse the matrix multiplication code more easily and make your main function more readable.
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Endnotes
Hope this article was helpful for you to understand matric multiplication in C. If you want to learn more about C programming and solidify your basics, you can explore our articles on C.
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Vikram has a Postgraduate degree in Applied Mathematics, with a keen interest in Data Science and Machine Learning. He has experience of 2+ years in content creation in Mathematics, Statistics, Data Science, and Mac... Read Full Bio
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