Multiply matrices of complex numbers using NumPy in Python

Last Updated : 23 Feb, 2023

In this article, we will discuss how to multiply two matrices containing complex numbers using NumPy but first, let's know what is a complex number. A Complex Number is any number that can be represented in the form of x+yj where x is the real part and y is the imaginary part. Multiplication of two complex numbers can be done using the below formula -

(a+ib) \times (x+iy)=ax+i^2by+i(bx+ay)=ax-by+i(bx+ay)

NumPy provides the vdot() method that returns the dot product of vectors a and b. This function handles complex numbers differently than dot(a, b).

Syntax:

numpy.vdot(vector_a, vector_b)

Example 1:

Python3

# importing numpy as library import numpy as np   # creating matrix of complex number x = np.array([2+3j, 4+5j]) print("Printing First matrix:") print(x)  y = np.array([8+7j, 5+6j]) print("Printing Second matrix:") print(y)  # vector dot product of two matrices z = np.vdot(x, y) print("Product of first and second matrices are:") print(z)

Output:

Printing First matrix: [2.+3.j 4.+5.j] Printing Second matrix: [8.+7.j 5.+6.j] Product of first and second matrices are: (87-11j)

Time complexity: O(1)
Auxiliary space: O(1)

Example 2: Now suppose we have 2D matrix:

Python3

# importing numpy as library import numpy as np   # creating matrix of complex number x = np.array([[2+3j, 4+5j], [4+5j, 6+7j]]) print("Printing First matrix:") print(x)  y = np.array([[8+7j, 5+6j], [9+10j, 1+2j]]) print("Printing Second matrix:") print(y)  # vector dot product of two matrices z = np.vdot(x, y) print("Product of first and second matrices are:") print(z)

Output:

Printing First matrix: [[2.+3.j 4.+5.j]  [4.+5.j 6.+7.j]] Printing Second matrix: [[8. +7.j 5. +6.j]  [9.+10.j 1. +2.j]] Product of first and second matrices are: (193-11j)

Time complexity: O(n^2), where n is the dimension of the matrices.
Auxiliary space: O(1), as the matrices and their product are stored in memory and no additional space is used.

Multiply matrices of complex numbers using NumPy in Python

hupphurr

Improve

Article Tags :

Practice Tags :

python

Multiply matrices of complex numbers using NumPy in Python

Similar Reads