## Diagonalizable & Minimal Polynomial

A matrix or linear map is diagonalizable over the field if and only if its minimal polynomial is a product of distinct linear factors over .

## Characteristic Polynomial

Let be an matrix. The characteristic polynomial of , denoted by , is the polynomial defined by

## Cayley-Hamilton Theorem

Every square matrix over a commutative ring satisfies its own characteristic equation:

If is an matrix, where .

Reblogged this on Project ENGAGE.

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Some proofs would be cool. Any models? Great stuff here

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Thanks for visiting! There are more theorems and some proofs here: https://mathtuition88.files.wordpress.com/2016/07/algebra-theorems-mathtuition88.pdf

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