# Matrices

Matrices are two dimensional arrays of numbers, e.g.

$\begin{bmatrix}1 & 2\\3 & 4\\5 & 6\end{bmatrix}$

describes a 3 by 2 matrix.

A matrix is described by the number of rows, then the number of columns.

## Matrix Multiplication

Matrix Multiplication is the process of multiplying two compatible matrices together. Unlike scalar multiplication, matrix multiplication is not commutative - that is, if a and b are matrices, $$a * b$$ is not guaranteed to produce the same matrix that $$b * a$$ produces.

In order to be compatible, the number of columns in matrix a must equal the number of rows in matrix b. This will produce a matrix that has the same number of rows as matrix a and the same number of columns as matrix b.

Note that this is also called the dot product.

Last updated: 2019-06-10 23:28:22 -0700