Thread: Eigenvalues

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?

I assume you meant "eigenvalues", not "eigenvectors". Hint: Consider the action of $\displaystyle AA^{-1}$ on an eigenvector of A.