Linear Algebra Review

Table of Contents:

Matrix Multiplication

Matrix Multiplication

$A \in R^{m\times n}$ $B \in R^{n\times p}$ $C=AB\in R^{m\times p}$

Where:

$C_{ij}=\sum_{k=1}^{n}A_{ik}B_{kj}$

Examples

$\begin{bmatrix} 1 & 2 & 3\\ 4 & 5 & 6 \end{bmatrix} \times \begin{bmatrix} 7 & 8\\ 9 & 10\\ 11 & 12 \end{bmatrix} = \begin{bmatrix} 58 & 64\\ 139 & 154 \end{bmatrix}$

import numpy as np
x = [[1, 2, 3],[4,5,6]]
y = [[7,8],[9,10],[11,12]]
np.dot(x, y)

#array([[ 58,  64],
#      [139, 154]])