16. Matrix by matrix multiplication, cont.

• Matrix by matrix multiplication, as well as matrix by vector multiplication, can be combined into a series of transformations. For example,

  • A · B · v

  where A and B are matrices, and v is a vector representing a point in space.

• Due to the associativity rules of multiplication (which applies similarly to C/C++ arithmetic operators), the above expression is interpreted as

  • ( A · B ) · v

  and is also equivalent to

  • A · ( B · v )

• The form ( A · B ) · v is preferred because it allows multiple transformations to be stored in a single matrix.

  See also: Chapter 6. Objects in Motion, Fun with Matrices article from Learning Modern 3D Graphics Programming tutorial