1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Show that if a is greater than or equal to the degree of minimal polyn

  1. Jan 30, 2014 #1
    1. The problem statement, all variables and given/known data
    Show that if a is greater than or equal to the degree of minimal polynomial (say k), then L^a is a linear combination of 1v,L,…,Lk−1

    If L is invertible, show the same for all a<0


    2. Relevant equations
    about minimal polynomial
    http://en.wikipedia.org/wiki/Minimal_polynomial_(linear_algebra [Broken])


    3. The attempt at a solution
    i know a few things about minimal polynomial, i know what linear combination, invertible means but i have no clue how to start this problem.

    i think the most confusing part i find is that i don't know how to deal with
    L^a and the 1_v,L,....,L^k-1
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jan 30, 2014 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper


    Read my response to your other question about minimal polynomials.
     
    Last edited by a moderator: May 6, 2017
  4. Jan 30, 2014 #3
    delete this post.
     
    Last edited: Jan 30, 2014
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Show that if a is greater than or equal to the degree of minimal polyn
  1. Show equality (Replies: 10)

Loading...