Linear Algebra proof

  • #1
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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?
 

Answers and Replies

  • #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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