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!

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..
    thx..
     
  2. jcsd
  3. May 21, 2009 #2

    D H

    User Avatar
    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Eigenvalues, detA
  1. Eigenvalues ? (Replies: 5)

  2. Imaginary Eigenvalues (Replies: 14)

Loading...