Matrix representation for transformation

[athrun200]

1. The problem statement, all variables and given/known data
See my blog
http://blog.yahoo.com/_HYUKNALCF4ULVTXY2JYSRAWDEA/articles/173228/index?bb=0


2. Relevant equations



3. The attempt at a solution
My attempt is also on the blog
http://blog.yahoo.com/_HYUKNALCF4ULVTXY2JYSRAWDEA/articles/173228/index?bb=0

[HallsofIvy]

I see nothing wrong with it. I was at first taken aback that you could do that with non-similar matrices but of course, saying that two matrices, A and B, are not similar only means there does not exist a single matrix, P, such that P^{-1}AP= B. Your Q is not the inverse of P.