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Question: Using Maple to prove invariance of trace

Question:Using Maple to prove invariance of trace

mzh 10 Maple
linear-algebra abstract
November 02 2011
0

Hallo

I'm new in Mapleprimes and I'm looking forward to interesting discussions.

I was just wondering if and how it would be possible to use Maple for something like proving invariance of trace under unitary transformation.

So

tr(\Omega) = tr(U^{+} O U)

and

U^{+}U = I

After a number of reformulations, one arrives at an expression tr(O) = tr(U \Omega U^{+}).

Another example would be to show that (AB)^{-1} = B^{-1}A^{-1}. This I show by using A^{-1}A = I. Is it possible to "teach" Maple this property, and then just "ask" if (AB)^{-1} = B^{-1}A^{-1} and Maple would then use the defined properties to carry out the proof.

Can this be done?

Thanks for any feedback
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