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 |
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 |
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!