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Homework Help: Eigenvalues, detA

  1. May 21, 2009 #1
    1. The problem statement, all variables and given/known data
    Let A be nxn matrix, suppose n has real eigenvalues,λ1,...,λn, repeated according to multipilicities. Prove that detA = λ1...λn.

    2. Relevant equations

    3. The attempt at a solution
    I started by applying the definition, Av = λv, where v is an eigenvector. then I just dun know how to keep going.. is there anyone can help me out? or at least give me some hints..
  2. jcsd
  3. May 21, 2009 #2

    D H

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    Staff Emeritus
    Science Advisor

    If matrices A and B are similar, what can you say about their determinants? Use this relationship to help you solve the problem.
  4. May 21, 2009 #3
    DH offered an correct approach,but you need to know something about similarity and Jordan normal form or Schur's lemma
    Here's another approach: consider the characteristic polynomial det(A-λI),by fundamental theorem of algebra, it can be factorized into (λ1-λ)(λ2-λ)........(λn-λ),then let λ=0 and see what will happen
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