In Linear Algebra, a by matrix is denoted as a grid of numbers with two brackets on either side. The variable corresponds to the number of rows, and the variable corresponds to the number of columns. The notation for a matrix is a shorthand way to write a system of linear equations.
A matrix represents a function that maps between two vector spaces. For example, the matrix below describes a function that maps between three space and two space. .
It is also common to use the variable to represent a matrix, the variable to represent the input vector, and the varaible to represent the output vector.