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Eigenvalues of Invertible Matrix

  1. Sep 5, 2014 #1
    1. The problem statement, all variables and given/known data
    If A is an invertible nxn matrix, then A has n distinct eigenvalues. (TRUE/ FALSE)



    2. Relevant equations



    3. The attempt at a solution
    True? We weren't really taught the concept of eigenvalues too well, but from what I can gather square matrices appear to have the same number of eigenvalues as their number of rows/columns. I'm not sure why though.
     
  2. jcsd
  3. Sep 5, 2014 #2

    AlephZero

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    Is the unit nxn matrix invertible? What are its eigenvalues?
     
  4. Sep 6, 2014 #3

    HallsofIvy

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    "number of eigenvalues" and "number of distinct eigenvalues" are two entirely different things. As far as being "invertible" is concerned the only thing you can say is that a matrix is invertible if and only if it does not have 0 as an eigenvalue.
     
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