Matrices

A matrix is a two dimensional array of components. For our purposes, those components are numbers or values.

A matrix can be a tool to manipulate Vectors or points. For example, a 2×2 matrix with trigonometry functions can rotate a point by a given angle about an axis. We put the coordinates of the point into the vector and multiply the matrix against the vector.

We can think of Matrix Multiplication as being a tool that can take an old vector and use it to make a new vector. We show an example below that mixes numbers and variables and it will be helpful in future things:

\begin{bmatrix} a & 0 \\ 0 & b \end{bmatrix} \begin{bmatrix} 1 \\ 1 \end{bmatrix} = \begin{bmatrix} a \\ b \end{bmatrix}