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:
