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Homework Help: Linear Algebra proof

  1. Sep 30, 2007 #1
    Assume that all eigenvalues of an nxn real matrix A have negative real parts. Show that the inverse of A exists.

    I really have no idea how to even start this one. Any hints?
     
  2. jcsd
  3. Sep 30, 2007 #2

    Dick

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    If the inverse of A doesn't exist, then there is an x such that Ax=0. Doesn't this mean it has an eigenvalue that DOESN'T have a negative real part?
     
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