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Cayley Hamilton Theorem says that a matrix $A$ satisfies its characteristic equation. My professor proved this for diagonalizable matrices. What happens if $A$ is not diagonalizable? Does the C-H Theorem still hold? Can you give a proof why it holds or why it does not?

Thanks!

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  • $\begingroup$ It does indeed hold in general $\endgroup$ – Aaron Zolotor Nov 2 '18 at 2:22
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    $\begingroup$ Yes, it still holds. One way to see this is to use the fact that diagonalizable matrices are dense in all matrices. $\endgroup$ – Qiaochu Yuan Nov 2 '18 at 2:22
  • $\begingroup$ @QiaochuYuan, can you please elaborate? $\endgroup$ – Nagabhushan S N Nov 2 '18 at 2:43
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It holds in general. Also the proof can be found in https://en.wikipedia.org/wiki/Cayley%E2%80%93Hamilton_theorem

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