Hi folks,

I have been bouncing my head off an algebraic problem, and it's become quite a headache.

The equation is

where

, and are all matrices (typically 4*4),

and are given and may be complex,

is the unknown to be solved for (will usually be required to be real), and

is an arbitrary nonzero scalar, I mean it can be any nonzero value that will make the two sides equal - in fact, the equation is a proportion.

I don't have a clue how to begin solving this. Even wrote it out term by term as sixteen huge scalar equations, but this didn't get me any closer.

Any ideas?