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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; December 12th 2011 at 04:50 PM.
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