PlanetMath: Cayley-Hamilton theorem

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Cayley-Hamilton theorem

(Theorem)

Let $T$ be a linear operator on a finite-dimensional vector space $V$ and let $c(t)$ be the characteristic polynomial of $T$ Then $c(T)=T_0$ where $T_0$ is the zero transformation. In other words, $T$ satisfies its own characteristic equation.

"Cayley-Hamilton theorem" is owned by akrowne.

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Attachments:: topological proof of the Cayley-Hamilton theorem (Proof) by rmilson
proof of Cayley-Hamilton theorem by formal substitutions (Proof) by asteroid
proof of Cayley-Hamilton theorem in a commutative ring (Proof) by Mathprof
lecture notes on the Cayley-Hamilton theorem (Topic) by rmilson

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Cross-references: characteristic equation, transformation, characteristic polynomial, vector space, finite-dimensional, linear operator
There are 11 references to this entry.

This is version 1 of Cayley-Hamilton theorem, born on 2002-02-05, modified 2002-02-05.
Object id is 1837, canonical name is CayleyHamiltonTheorem.
Accessed 17336 times total.

Classification:

AMS MSC:	15A15 (Linear and multilinear algebra; matrix theory :: Determinants, permanents, other special matrix functions)
	15A18 (Linear and multilinear algebra; matrix theory :: Eigenvalues, singular values, and eigenvectors)

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