Matrices are commonly used to represent transformations, which are discussed
later.
They are generally a two-dimensional representation with a given number of
rows and columns.
So, using standard nomenclature, an 
matrix has N rows and
M columns, each entry of which is a number.
An example 
matrix 
is:
One often summarizes the notation of a matrix by saying 
is 
, referring to the 
entry of the matrix
( i.e. the entry at the 
row and 
column).
For vision purposes, most arrays are square, meaning that they have the same number of rows and columns.
Multiplying, or finding the product of two matrices is a common operation.
Let 
be a 
matrix and
be a 
matrix.
Then, the matrix 
that is their product is a 
matrix.
If 
is 
and 
is 
, then
the entries of 
are given by:
A special matrix is the identity matrix 
,
which is a square matrix containing all zeros except along the
top-left to bottom-right diagonal (called the main diagonal),
which has the value one at each diagonal position.
Here is the 
identity matrix:
The identity matrix is a special case of a diagonal matrix, which contains zeros at all locations except along the main diagonal. Here is a diagonal matrix:
For each matrix 
, there is a special matrix called the
inverse of 
, and is often denoted 
.
This matrix has the property:
In the case of 
matrices, if the matrix 
is:
then the inverse of 
is:
The product of matrices is not commutative, which means that, in general,
(although sometimes they are equal for particular matrices). However, matrix products are associative, which means:
