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.
# 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 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!