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Math Forum » Discussions » sci.math.* » sci.math.num-analysis.independent

Topic: Commuting matrices as polynomials?
Replies: 5   Last Post: Feb 20, 2008 4:46 PM

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jw12jw12jw12@yahoo.com

Posts: 37
Registered: 10/27/05
Re: Commuting matrices as polynomials?
Posted: Feb 20, 2008 4:46 PM
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On Feb 20, 3:52 pm, Robert Israel
<isr...@math.MyUniversitysInitials.ca> wrote:

> > There's just one step in your explanation I don't follow (the "wlog"
> > part). A,B, and C are commuting matrices and you want to see if A and
> > B are expressible as polynomials in C. I see that adding a multiple of
> > I to C will not affect the commutativity, but then A and B won't
> > necessarily be polynomials in C+kI. Isn't that a problem?
>
> Huh? If A = f(C) where f is a polynomial, then A = h(C+kI) where
> h(t) = f(t-k) is again a polynomial.
> --
> Robert Israel isr...@math.MyUniversitysInitials.ca
> Department of Mathematics http://www.math.ubc.ca/~israel
> University of British Columbia Vancouver, BC, Canada

Doh! I had a feeling I was saying something dumb.

jw

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