Matrix Symbol

In Linear Algebra, a matrix is denoted as a grid of numbers with two brackets on either side.

Notation

A matrix represents a function that maps between two vector spaces. For example, the matrix below describes a function that maps between three dimensions and three dimensions. .

A matrix is a function that maps between two vector spaces. This image shows how the input correlates with each column and that the output is the result of summing the contents each row.

In this case the input to the function is the three numbers (x,y,z) and the output of the function three numbers (x*, y*, z*). The asterix is used to show that the output numbers are different from the input numbers. The letters a, b, …, i, j are variables that represent numbers. This is equivelent to the system of equations below:

Basic Usage

Some fundemental uses of a matrix is in scaling and rotating functions in two-dimensions. Take for example this square drawn in , we can transform it using the matrix A: