Question

Why is it that a nxn matrix has at most n eigenvalues?

Answer 1

Don't know if you have come across this before:

http://en.wikipedia.org/wiki/Characteristic_polynomial

Answer 2

No, but that page is not helping i think... I know it has something to do with the linearly independce of the n colloms in the matrix, but not the direct conclusion.

Answer 3

Well, the main point is that the characteristic equation is calculated with reference to the determinant so you will end up with an eigenvalue equation whose degree is 2 for a 2 by 2, 3 for a 3 by 3 and so on.

Such an equation has number of roots equal to the degree which is equal to n.

Answer 4

I see it now, thanks. But that is not how i should clarify it, because i cannot use that rule yet according to the study guide.