Show that A and A^{T} have the same eigenvalues. what if anything can we say about the associated eigenvectors of A and A^{T}?

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- Apr 10th 2009, 08:01 PMantmaneigenvalues
Show that A and A^{T} have the same eigenvalues. what if anything can we say about the associated eigenvectors of A and A^{T}?

- Apr 11th 2009, 12:02 AMmr fantastic
.

The eigenvectors of are generally different to those of . However, there is a relationship between the two:

If is an eigenvector of corresponding to the eigenvalue and is an eigenvector of corresponding to the eigenvalue then .

**Proof:**

.... (1)

.... (2)

(1) - (2): and the result is easily seen.