Let l1,l2 . . . ,ln be the eigenvalues of a matrix A. What are the eigenvalues of A^2?

there must be some relation bwn. the eigenvalues of A and A^2 matrix which i cannot see it.. Please assist.

Many thanks.

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- Sep 8th 2009, 10:07 AMsaskadimovaeigenvalues of qudratic matrixLet l1,
*l*2 . . . ,*l*n be the eigenvalues of a matrix A. What are the eigenvalues of A^2?

there must be some relation bwn. the eigenvalues of A and A^2 matrix which i cannot see it.. Please assist.

Many thanks.

- Sep 8th 2009, 12:10 PMThePerfectHacker
- Sep 8th 2009, 12:16 PMBruno J.
Suppose is an eigenvalue associated to some vector ; then , and , so is an eigenvalue of .

Note that the converse does not always hold; could have no eigenvalues while could. For instance if rotates the plane by an angle of , then has no (real) eigenvalues but does.