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Spectral Radius Inequality for Matrix Products

Thread starter defunc
Start date Apr 10, 2011
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Inequality Matrix Radius

Apr 10, 2011

#1

defunc

Hi,

Does the following inequality hold regarding the product of 2 matrices A and B: p(AB) <= p(A)p(B), where p denotes the spectral radius.

Thanks!

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Apr 10, 2011

#2

Hurkyl

Staff Emeritus

Science Advisor

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Have you tried anything to prove it? Intuitively why do you think it should be true?

Thread 'About the existence of Hamel basis for vector spaces'

It is well known that a vector space always admits an algebraic (Hamel) basis. This is a theorem that follows from Zorn's lemma based on the Axiom of Choice (AC). Now consider any specific instance of vector space. Since the AC axiom may or may not be included in the underlying set theory, might there be examples of vector spaces in which an Hamel basis actually doesn't exist ?

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