Let A be an nxn matrix with eigenvalue ∆ with multiplicity n. Show that A is diagonizable iff A=∆I, where I is the nxn idenity.

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- Apr 26th 2010, 08:51 AM #1

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- Apr 26th 2010, 09:07 AM #2

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$\displaystyle \Delta$ eigenvalue of $\displaystyle A$ of multiplicity $\displaystyle n\iff (x-\Delta)^n$ is the charateristic pol. of $\displaystyle A$ , and thus $\displaystyle A$ is diagonalizable $\displaystyle \iff x-\Delta$ is the minimal pol. of $\displaystyle A\iff A=\Delta I $ .

Tonio

- Apr 26th 2010, 10:38 AM #3

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- Apr 27th 2010, 02:20 AM #4

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