Hello this is Gulshan Negi
Well, matrix multiplication is a mathematical operation used to combine two matrices to produce a third matrix. It involves multiplying the elements of one matrix by the elements of another matrix and adding up the results.
How matrix multiplication works:
Suppose we have two matrices, A and B. Matrix A has dimensions m x n (m rows and n columns), while matrix B has dimensions n x p (n rows and p columns). To multiply these matrices, we need to make sure that the number of columns in matrix A is equal to the number of rows in matrix B.
The resulting matrix, C, will have dimensions m x p (m rows and p columns). Each element of the resulting matrix is computed as the dot product of a row from matrix A and a column from matrix B. To find the element at the ith row and jth column of the resulting matrix, we would multiply the elements in the ith row of matrix A by the elements in the jth column of matrix B and add up the results.
This can be represented mathematically as:
C(i,j) = sum(A(i,k) * B(k,j)) for k=1 to n
Codebase-
def matrix_multiplication(A, B):
m, n = A.shape
n, p = B.shape
C = np.zeros((m, p))
for i in range(m):
for j in range(p):
for k in range(n):
C[i,j] += A[i,k] * B[k,j]
return C
where A and B are the input matrices, and np is the NumPy library used for matrix operations.
Hope it will help you.
Thanks