Matrix Math

Matrix Math centers around Dot Product and Matrix Multiplication.

Also see Linear Algebra: Matrices for mathematical references

Dot Product

The dot product of a matrix is the multiplication of 2 matrices.

np.dot() is a legacy numpy method that allows for consistent matrix multiplication up to 2D matrices.

np.matmul is the new method used for matrix multiplication in numpy, allowing for batched matrix multiplication.

Rules of matrix multiplication must be followed when using np.matmul()

"""
Let's say we have the following matrices:
 
x: [1 2 3] 
y: [6 7 8] 
A: [[1 2 3] 
    [4 5 6] 
    [7 8 9]] 
B: [[1 4 3] 
    [6 4 3] 
    [9 4 3]]
"""
 
np.matmul(x, y)
> 44
 
np.matmul(A, B)
>[[ 40 24 18] 
  [ 88 60 45] 
  [136 96 72]]
 
np.matmul(B, A)
> [[38 46 54]
   [43 56 69]
   [46 62 78]]

Broadcasting

Matrix Broadcasting also happens in matrix calculations.

np.matmul(A, x)
> [14 32 50]
 
np.matmul(x, A)
> [30 36 42]

Refer to Linear Algebra: Matrices to understand how this works.

Transposition

Transposition changes the axis of a given matrix.

import numpy as np  
  
A = np.array([[1,2,3],  
              [4,5,6]]).T
> [[1  4]
   [2  5]
   [3  6]]

If A is of an (n,m) shape, then A^T is of (m,n) shape.