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