Game Development Reference
In-Depth Information
Subtraction is the same, except the components are subtracted. Both of these op-
erations rarely see use in games.
Scalar Multiplication
As can be done with vectors, it is possible to multiply a matrix by a scalar.
Multiplication
Matrix multiplication is an operation that sees widespread use in games. The easi-
est way to visualize matrix multiplication between two matrices with the same
dimensions is to think in terms of vectors and dot products. Suppose you have
matrices
A
and
B
, as shown here:
To calculate
C
=
A×B
, take the first row of
A
and dot product it with the first
column of
B
. The result of this dot product is the top-left value in
C
. Then dot
product the first row of
A
with the second column of
B
, which gives the top-right
value in
C
. Repeat this process for the second row of
A
to complete the multiplic-
ation.
Matrix multiplication does not require matrices to have identical dimensions, but
it does require that the number of columns in
A
be equal to the number of rows in
B
. For instance, the following multiplication is also valid:
Multiplying two4×4matrices followsthesameprinciple assmaller ones;thereare
just more elements to calculate:
