
Re: Commuting matrices as polynomials?
Posted:
Feb 20, 2008 4:46 PM


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(tk) 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

