Game Development Reference
In-Depth Information
It is important to note that matrix multiplication is
not
commutative, though it is
associative and distributive over addition:
Another important property of matrix multiplication is the
identity matrix
. If you
multiply a scalar value by 1, it does not change. Similarly, multiplying a matrix by
the identity matrix
I
does not change the matrix's value.
A
=
A
×
I
The identity matrix has a number of rows and columns equal to the number of
columns in
A
, and values within the identity matrix are all zeroes except for a di-
agonal of ones. Therefore, a 3×3 identity matrix looks like this:
Inverse
If a matrix is multiplied by its inverse, denoted by
-1
, the result is the identity mat-
rix:
I
=
A
×
A
-1
