Drexel dragonThe Math ForumDonate to the Math Forum


Math Forum
 Ask Dr. Math
 Discussions
 Internet Newsletter
 MathTools
 Problems of the Week
 Teacher2Teacher
 Teacher Exchange
 Workshops

Search All of the Math Forum:
Browse our Internet Mathematics Library

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

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

Advanced Search
Reply to this Topic Reply to this Topic

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Steve Lord

Posts: 611
Registered: 12/6/04
Re: polynomial degree
Posted: Jan 2, 2001 10:26 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply



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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2013. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.