Thread: matrix math

Show that if A = QR with Q invertable, then A is similar to A1 = RQ?


The hint I have is:
Find an invertible matrix P so that RQ = P^-1AP.

I need more help please.


jack

You're told that Q is invertible (Q^-1 exists) and you need to conjugate
A by something, ie map A -> P^-1AP for some P. About the only P you
know of which is invertible is Q, so why not try that? Q^-1 A Q = Q^-1 QR Q = ...

I think that will work.