A matrix F is a rectangular array of numbers (elements) that has N rows and M columns (matrix with size N x M).  For example, here is a 3 x 4 matrix:


Matrices have fundamental importance in any graphics engine.  Matrices are typically used to represent transformations (e.g., between coordinate systems, rotation, scale, translation, etc.). 

Matrices for which N = M are called square.  In graphics programming, matrices are often square, with size 3 x 3 or 4 x 4.

A vector is simply a matrix with N or M equal to 1.  For example, this is column vector is a 3 x 1 matrix:



Two matrices are equal if and only if all elements are equal.  Note this requires the matrices have the same size.  For example:

High