Originally Posted by

**GClements**
A matrix whose columns are the world-space T,B,N vectors transforms from tangent space to world space. Its inverse (which is the same as the transpose provided that the matrix is orthonormal) transforms from world space to tangent space. Lighting calculations can be done in either space. You can either transform the normal from the normal map from tangent space to world space, or the eye and light vectors from into tangent space. But if you're doing raytracing, you'd want the reflection vector in world space.