Python Program to multiply two matrices

Given two matrices, the task to multiply them. Matrices can either be square or rectangular.

Examples:

Input : mat1[][] = {{1, 2}, 
                   {3, 4}}
        mat2[][] = {{1, 1}, 
                    {1, 1}}
Output : {{3, 3}, 
          {7, 7}}
Input : mat1[][] = {{2, 4}, 
                    {3, 4}}
        mat2[][] = {{1, 2}, 
                    {1, 3}}       
Output : {{6, 16}, 
          {7, 18}}

Multiplication of Square Matrices : 
The below program multiplies two square matrices of size 4*4, we can change N for different dimensions. 

Python3

# 4x4 matrix multiplication using Python3
# Function definition
def matrix_multiplication(M, N):
    # List to store matrix multiplication result
    R = [[0, 0, 0, 0],
        [0, 0, 0, 0],
        [0, 0, 0, 0],
        [0, 0, 0, 0]]

    for i in range(0, 4):
        for j in range(0, 4):
            for k in range(0, 4):
                R[i][j] += M[i][k] * N[k][j]

    for i in range(0, 4):
        for j in range(0, 4):
            # if we use print(), by default cursor moves to next line each time,
            # Now we can explicitly define ending character or sequence passing
            # second parameter as end ="<character or string>"
            # syntax: print(<variable or value to print>, end ="<ending with>")
            # Here space (" ") is used to print a gap after printing
            # each element of R
            print(R[i][j], end =" ")
        print("
", end ="")

# First matrix. M is a list
M = [[1, 1, 1, 1],
    [2, 2, 2, 2],
    [3, 3, 3, 3],
    [4, 4, 4, 4]]

# Second matrix. N is a list
N = [[1, 1, 1, 1],
    [2, 2, 2, 2],
    [3, 3, 3, 3],
    [4, 4, 4, 4]]

# Call matrix_multiplication function
matrix_multiplication(M, N)

# This code is contributed by Santanu

Output

Result matrix is 
10 10 10 10 
20 20 20 20 
30 30 30 30 
40 40 40 40

Time complexity: O(n³). It can be optimized using Strassen’s Matrix Multiplication

Auxiliary Space: O(n²)

Multiplication of Rectangular Matrices : 
We use pointers in C to multiply to matrices. Please refer to the following post as a prerequisite of the code.
How to pass a 2D array as a parameter in C?

Python3

# Python3 program to multiply two
# rectangular matrices

# Multiplies two matrices mat1[][]
# and mat2[][] and prints result.
# (m1) x (m2) and (n1) x (n2) are
# dimensions of given matrices.
def multiply(m1, m2, mat1,
             n1, n2, mat2):

    res = [[0 for x in range(n2)]
              for y in range (m1)]

    for i in range(m1):
        for j in range(n2):
            res[i][j] = 0
            for x in range(m2):
                res[i][j] += (mat1[ i][x] *
                              mat2[ x][j])

    for i in range(m1):
        for j in range(n2):
            print (res[i][j],
                   end = " ")
        print ()

# Driver code
if __name__ == "__main__":

    mat1 = [[2, 4], [3, 4]]
    mat2 = [[1, 2], [1, 3]]
    m1, m2, n1, n2 = 2, 2, 2, 2

    # Function call
    multiply(m1, m2, mat1,
             n1, n2, mat2)

# This code is contributed by Chitranayal

Output

6 16 
7 18

Time complexity: O(n³). It can be optimized using Strassen’s Matrix Multiplication

Auxiliary Space: O(m1 * n2)

Please refer complete article on Program to multiply two matrices for more details!