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Topic: polynomial degree
Replies: 8   Last Post: Jan 3, 2001 2:46 PM

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 Steve Lord Posts: 611 Registered: 12/6/04
Re: polynomial degree
Posted: Jan 2, 2001 10:26 AM

On Tue, 2 Jan 2001 euclid2000@my-deja.com wrote:

> Hi !
>
> Given ARBITRARY n-by-n matrices A_i, i=0,....,d then
> p(t):= det( A_0 + t*A_1+.....+t^d*A_d) is a polynomial
> in t. What can we say about the degree of p(t) ? An upper
> bound is deg(p) <= d*n but I would like to obtain an exact
> value depending on the A_i's (rank and structure?).

Let A_i = the nxn identity for all i's. Then, you're pretty well stuck
with p(t) = 1 +t^n + t^(2*n) ... + t^(d*n), if I've done the calculation
correctly. So, we can attain the upper bound.

If you knew something more about the matrices then you might be able to
figure something out.

Steve L

Date Subject Author
1/2/01 euclid2000@my-deja.com
1/2/01 Steve Lord
1/2/01 Steve Lord
1/2/01 David C. Ullrich
1/2/01 Robert Israel
1/2/01 Virgil Hancher
1/3/01 David C. Ullrich
1/3/01 Virgil Hancher
1/2/01 Dr. Uwe Prells