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Eigenvalue and invertible matrices

  1. Dec 3, 2008 #1
    How do I prove that if A is an invertible matrix and lambda does not equal zero then one dived by lambda is an eigenvalue of the inverse of A?
     
  2. jcsd
  3. Dec 3, 2008 #2

    Ben Niehoff

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    Gold Member

    First of all, if A is invertible, then none of the eigenvalues can be 0, by definition.

    Second, consider

    [tex]Av = \lambda v[/tex]

    for some eigenvector v. What is

    [tex]A^{-1}(\lambda v)[/tex]

    ?
     
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