What's a pre-multiplied 4x4 matrix?

I'm using a 3d game engine, that uses a 4x4 matrix to modify the camera projection.

The matrix is in the regular 4x4 format:

 r r r  x
r r r  y
r r r  z
- - -  zoom


The description for the matrix class says:

A transformation matrix. Matrices are pre-multiplication, as in: x' = M*x.

What does this mean?

• There is no regular 4x4 matrix format, only row- and column-major form. Your example is in column-major form, as used for instance in OpenGL. – Maik Semder Jan 14 '12 at 16:41
• Check this link. It's explained in detail: scratchapixel.com/lessons/3d-basic-lessons/lesson-4-geometry/… – user14697 Mar 24 '12 at 23:05

It's not saying the matrices are pre-multiplied but rather that they are (read use) pre-multiplication.

This basically specifies the correct order of multiplication when using them, such that when multiplying a matrix by a vector, the matrix needs comes first.

In other words, this:

result = matrix * vector


result = vector * matrix