Matrix Multiplications

Lesson 18 of 18 in Coddy's Numpy Fundamentals course.

Matrix multiplication is a series of dot products that produce a new matrix.

How it works?

Assume we have two matrices A with the shape of (3, 2) and B with the shape (2, 4).

The multiplication of A and B will give a new matrix with the shape (3, 4).

The inner shapes of the matrices must match (in this case both A and B have 2 -> (3,2)(2,4)=(3,4))

multiplication of A*b is the

dot product of Row 1 of A with Column 1 of B is the result of the element at [1, 1]
dot product of Row 1 of A with Column 2 of B is the result of the element at [1, 2]
...
...
dot product of Row 2 of A with Column 1 of B is the result of the element at [2, 1]
dot product of Row 2 of A with Column 2 of B is the result of the element at [2, 2]
...
...
etc.

Example:

Matrix A:

1	2
3	4
5	6

Matrix B:

7	8	9	10
11	12	13	14

Result:

17 + 211	18 + 212	19 + 213	110 + 214
37 + 411	38 + 412	39 + 413	310 + 414
57 + 611	58 + 612	59 + 613	510 + 614

And after calculating:

29	32	35	38
65	72	79	86
101	112	123	134

How to do it in numpy?

There are 3 ways to multiply matrices:

np.matmul(matrix1, matrix2)
matrix1.dot(matrix2)
A @ B

import numpy as np
A = np.array([[1, 2], [3, 4], [5, 6]])
B = np.array([[7, 8, 9, 10], [11, 12, 13, 14]])
np.matmul(A,B)

Output:

array([[ 29,  32,  35,  38],
       [ 65,  72,  79,  86],
       [101, 112, 123, 134]])

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

Challenge

Create a function called matrix_master that receives three python lists and return the matrix multiplication of the first two lists and perform a dot product of the result with the last list

Try it yourself

import numpy as np
def matrix_master(lst1, lst2, lst3):
    # complete

All lessons in Numpy Fundamentals

1Introduction

What is Numpy?Numpy Core Array Constraints

4Arithmetic

Simple Operations Dot ProductMatrix Multiplications

2N-Dimensional Array Creation

Higher Dimension Understanding Shapes Populate with Fixed Values Numpy Types Range Reshape

3Indexing Numpy Array

Basic Indexing Slicing Array Indexing Dimensional Indexing Boolean Indexing Multiple Condition Indexing

17 + 211	18 + 212	19 + 213	110 + 214
37 + 411	38 + 412	39 + 413	310 + 414
57 + 611	58 + 612	59 + 613	510 + 614