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 –
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 libraryimport numpy as np# creating matrix of complex numberx = 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 matricesz = 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 libraryimport numpy as np# creating matrix of complex numberx = 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 matricesz = 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.
