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From: Stephen Montgomery-Smith on 15 Jun 2010 20:08
Arturo Magidin wrote:

> Yes, the assertion is true if the matrix is diagonalizable, or if the
> characteristic polynomial splits, or if the matrix has a Jordan form
> (which of course includes the diagonalizable case); just not in
> general for even the real numbers. Of course, adding hypothesis may
> make it true (like adding the missing "matrix is symmetric"), but *as
> stated* it was false.
>
> --
> Arturo Magidin

Here is a question I have wondered about. Suppose that A is a symmetric
matrix over an algebraically closed field (not necessarily the complex
numbers). Does it follow that A is diagonalizable?

Stephen
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