Let me try to explain it a little better.
I need to export a model from Blender, in which the z axis faces up, into OpenGL, where the y axis faces up.
For every coordinate (x, y, z) it’s simple; just swap the y and z values: (x, z, y).
Because I have swapped the all the y and z values, any matrix that I use also needs to be flipped so that it has the same effect.
After a lot of searching I’ve eventually found a solution at gamedev:
If your matrix looks like this:
{ rx, ry, rz, 0 }
{ ux, uy, uz, 0 }
{ lx, ly, lz, 0 }
{ px, py, pz, 1 }
To change it from left to right or right to left, flip it like this:
{ rx, rz, ry, 0 }
{ lx, lz, ly, 0 }
{ ux, uz, uy, 0 }
{ px, pz, py, 1 }