hi limpfisch,

It's a looooong time since I did this so I'm having to drag this up from deep memory.

A pair of vectors form a basis (let's say for C) if you can always find scalars so that

In the new basis

So you need these to be equal.

times by the inverse of the right hand matrix

gives

So, coordinates in the old basis are turned into coordinates in the new basis by this matrix.

Hopefully that is correct ... fingers crossed ...

Bob