# 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`

.

See this explanation until I write up a better one.

Note that this is also called the dot product.