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

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- July 28th 2005, 07:21 AMjackbell123What!
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 - August 1st 2005, 11:10 AMrgep
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 = ... - August 2nd 2005, 08:45 AMjackbell123
I think that will work.