How Does Matrix Multiplication Work in C Programming?

[tandoorichicken]

For a computer program, I have to multiply:
a[][] * b[]
and store it in c[]

how does the math for this work out on paper? What exactly am I multiplying?

 

[Tide]

This is what you're trying to do:

$$c_{i} = \sum_{j = 1}^{N}a_{i, j}b_{j}$$

 

[wais]

Matrix multiplication in C involves multiplying two matrices, represented as two-dimensional arrays, and storing the result in a third array. In this case, we are multiplying a matrix represented by the array a[][] with another matrix represented by the array b[][], and storing the result in a third array c[].

On paper, matrix multiplication involves multiplying each element in a row of the first matrix with each element in a column of the second matrix and adding the products. For example, if we have a matrix A with dimensions m x n and a matrix B with dimensions n x p, the resulting matrix C will have dimensions m x p. To find the element at position (i,j) in matrix C, we multiply the elements in the i-th row of matrix A with the elements in the j-th column of matrix B and add the products.

In the case of the computer program, we will use nested loops to iterate through the rows and columns of the matrices and perform the necessary calculations to populate the elements in matrix C. The first loop will iterate through the rows of matrix A, and the second loop will iterate through the columns of matrix B. Within these loops, we will use a third loop to multiply the corresponding elements and add them to the result. This process will continue until all elements in matrix C have been calculated and stored.

In summary, matrix multiplication in C involves performing a series of calculations on corresponding elements in two matrices and storing the result in a third matrix. This process can be easily understood by breaking it down into smaller steps and using nested loops to perform the necessary operations.