Coord Transformation

It's a matrix multiplication...

Your new coordinate systems basis vectors X, Y, Z will be used to create a transformation matrix...

Can you explain this thing a little more detailed?
:-(

Think of the "standard" 3d coordinate space... you have an x-axis (basic vector <1, 0, 0, 0>), a y-axis (basis <0, 1, 0, 0>), and a z-axis (basic <0, 0, 1, 0>).

Pretend you want to transform the coordinate to a coordinate space where the y axis becomes x, the z-axis becomes y, and the and the x-axis becomes z.

You would multiply by this matrix...
|0 1 0 0| <-"x" basis
|0 0 1 0| <-"y" basis
|1 0 0 0| <-"z" basis
|0 0 0 1|

If you want to translate the coordinate frame as well, the 0 at the end of each basis should become the negative dot product of the vector3 position of the camera and the vector3 of the basis itself.