Is 1/λ an Eigenvalue of the Inverse of A?

Thread starter stine23
Start date Dec 3, 2008
Tags

Eigenvalue Matrices

Dec 3, 2008

stine23

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?

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Dec 3, 2008

Ben Niehoff

Science Advisor

Gold Member

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

Second, consider

Av = \lambda v

for some eigenvector v. What is

A^{-1}(\lambda v)

?

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