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Topic: Unitary equivalence of real matrices
Replies: 1   Last Post: Feb 26, 2013 11:13 AM

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Jose Carlos Santos

Posts: 4,896
Registered: 12/4/04
Re: Unitary equivalence of real matrices
Posted: Feb 26, 2013 11:13 AM
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On 26-02-2013 15:19, José Carlos Santos wrote:

> Let A an B be two square matrices over the reals with the same size and
> suppose that they are unitarily equivalent, that is, that there is an
> unitary matrix U such that U.A.U^{-1} = B. Does it follow that there is
> an orthogonal real matrix M such that M.A.M^{-1} = B?

Forget about it. The answer is "yes" and this is proved in Halmos'
problem book in Linear Algebra.

Best regards,

Jose Carlos Santos

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