Α1,A2, …An are the eigenvectors of A (with algebraic multiplicity) the 1/A1, 1/A2, …,1/A n are the eigenvalues of A^-1 (with algebraic multiplicity)

how would i show this? any suggestions?

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- Apr 30th 2011, 01:45 PMkeelejodyEigenvalues
**Α1,**A2, …An are the eigenvectors of A (with algebraic multiplicity) the 1/A1, 1/A2, …,1/A n are the eigenvalues of A^-1 (with algebraic multiplicity)

how would i show this? any suggestions? - Apr 30th 2011, 06:07 PMTinyboss
I assume you meant "eigenvalues", not "eigenvectors". Hint: Consider the action of $\displaystyle AA^{-1}$ on an eigenvector of A.