Results 1 to 1 of 1

Thread: Multiplicity Homework Problem

  1. #1
    Junior Member
    Feb 2011

    Multiplicity Homework Problem

    I was wondering if I could have help with the following problem:
    Let A be an n by n matrix and let lambda be an eigenvalue of A whose eigenspace has dimension k, where 1<k<n. Show that lambda is an eigenvalue of A with multiplicity at least k.
    I'm supposed to use the following theorem:
    If B is similar to A, then A and B have the same eigenvalues (the solutions to both of their characteristic equations are the same).
    Relevant fact: I know that because A is n by n that A has n linearly independent column vectors. Does this have anything to do with A having k linearly dependent eigenvectors?
    Last edited by charmedquark; Dec 12th 2011 at 04:50 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. eigen value geometric multiplicity problem
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Nov 10th 2011, 10:40 AM
  2. eigenvalues --- multiplicity
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 14th 2011, 03:31 PM
  3. Multiplicity Problem.
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Jan 20th 2011, 03:54 AM
  4. Multiplicity of a root
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 1st 2010, 07:09 AM
  5. Multiplicity of roots
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: Mar 26th 2007, 10:15 AM

Search Tags

/mathhelpforum @mathhelpforum