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Eigenvectors, Eigenvalues and Idempotent

  1. Nov 20, 2005 #1

    mpm

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    I have a question that deals with all three of the terms in the title. I'm not really even sure where to begin on this. I was hoping someone could help.

    Question:

    An n x n matrix A is said to be idempotent if A^2 = A. Show that if λ is an eigenvalue of an independent matrix, then λ must either be 0 or 1.

    If I could get some help on this I would really appreciate it.

    Thanks,

    mpm
     
  2. jcsd
  3. Nov 20, 2005 #2
    Well you know that there must exist a nonzero vector v such that A*v=lamda*v. Now play with this statement by applying A again, and rearanging terms so that you end up with only expressions involving lambda. Then solve for lambda.
     
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