Matrix Multiplication in Python

Introduction

A double rectangular array of data represented in rows and columns is known as a Python matrix. A matrix's data might consist of letters, integers, strings, formulas, symbols, etc. One of the crucial data structures that may be employed in calculations in math and science is the matrix.

By multiplying the rows of the first matrix by the columns of the second matrix, NumPy matrix multiplication creates a single matrix from two input matrices. NumPy has three alternative routines for multiplying two matrices.

numpy.multiply(board_arr1, board_arr2) – Element based multiplication
numpy.matmul(board_arr1, board_arr2) – Product of two matrices
numpy.dot(board_arr1, board_arr2) – Scalar/dot product

Ensure that the first matrix's first column and second matrix's second row totals are equal before performing matrix multiplication in NumPy.

Quick Reference

Here are a few brief examples of NumPy matrix multiplication in case you're in a hurry.

# basic matrix multiplication
board_arr2 = np.multiply(arr, board_arr1)

# multiply specific rows multiplication
board_arr2 = np.multiply(arr[ 0,: 2], board_arr1[ 1,: 2])

# dot product arr = np.array([[1, 3 ],[4, 1 ]])
board_arr1 = 2
board_arr2 = np.dot(arr,board_arr1)

# product of two arrays
board_arr2 = np.dot(arr,board_arr1)

# standard product

board_arr2 = np.matmul(arr,board_arr1)

1. NumPy.multiply()

Let's create some NumPy arrays and use them to multiply things element by element with the NumPy.multiply() function. This uses element-wise multiplication, also known as the Hadamard product, to multiply each element of the first matrix by its corresponding element in the second matrix. To multiply, make sure that both matrices have the same dimensions.

import numpy as np
# Create a numpy two dimensional arrays
my_board_arr1 = np.array([

[2, 4, 3, 1],

[2, 3, 6, 1]

])
my_board_arr2= np.array([

[2, 1, 5, 2],

[4, 8, 3, 2]

])

# Use numpy.mutiply() function and
# get the matrix multiplication
my_board_arr3= np.multiply(my_board_arr1,my_board_arr2)
print(my_board_arr3)

# Output :
# [[ 4 4 15 2]
# [ 8 24 18 2]]

write your code here: Coding Playground

To supply a set of columns, rows, or submatrices to the numpy. Utilize the multiply() function to multiple certain rows, columns, and submatrices. The sizes of the submatrices, columns, and rows that we supply as our operands should be followed. Take this as an example:

# Get the certain rows multiplication
board_arr2 = np.multiply(arr[ 0,: 2], board_arr1[ 1,: 2])
print(board_arr2)

# Output :
# [ 5 12]

board_arr3 = np.multiply(arr[ 1,: 3], board_arr1[ 0,: 3])
print(board_arr3)

# Output :
# [ 2 8 18]

2. NumPy.dot()

Scalar multiplication is a straightforward method of multiplying matrices, and we can accomplish this using the NumPy dot() function. A scalar can be multiplied by a matrix, or a matrix can be multiplied by a scalar, in scalar multiplication. The scalar is multiplied by each member of the matrix to produce an array with the same form as the original array. Order is irrelevant when conducting scalar multiplication.

# Get dot product of arrays
arr = np.array([[1, 3 ],
[4, 1 ]])
board_arr1 = 2
board_arr2 = np.dot(arr,board_arr1)
print(board_arr2)

# Output :
# [[2 6]
# [8 2]]

Using np.dot, we may multiply a two-dimensional matrix by another two-dimensional matrix (). When multiplying two matrices, the operations should be performed in the correct sequence; for example, multiplying matrix X by matrix Y does not yield the same result as multiplying matrix Y by matrix X.

# Create numpy arrays
arr = np.array([[1, 3],
[4, 1]])

board_arr1 = np.array([[1, 2],
[2, 5]])

board_arr2 = np.dot(arr,board_arr1)
print(board_arr2)

# Output :
# [[ 7 17]
# [ 6 13]]

write your code here: Coding Playground

3. matmul()

In order to determine the matrix product of two arrays, use the np.matmul() function. The NumPy arrays' matrix multiplication is returned by the matmul() method, which accepts the inputs board_arr1 and board_arr2. Only when board_arr1 and board_arr2 are both 1-dimensional vectors is a scalar generated.

# Use numpy.matmul() function
# Get the product
board_arr2 = np.matmul(arr,board_arr1)
print(board_arr2)

# Output :
# [[ 7 17]
# [ 6 13]]

Conclusion

In this article, we have covered the idea of NumPy matrix multiplication in Python as well as how to use it with examples using the functions numpy.multiply(), numpy.matmul(), and numpy.dot().