Every square matrix satisfies its own characteristic polynomial. Named for Arthur Cayley and William Rowan Hamilton, it is a basic structural fact of linear algebra with wide use in matrix computation.
Facts
StatementThe Cayley-Hamilton theorem states that every square matrix over a commutative ring satisfies its own characteristic equation. 1 Classification
Statement Form Connections
Sources
1. Cayley-Hamilton Theorem (Wikipedia)
Wikimedia FoundationLead section, opening sentence
In linear algebra, the Cayley-Hamilton theorem (named after the mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix over a commutative ring (such as the real or complex numbers or the integers) satisfies its own characteristic equation.
History section, on Frobenius's general proof
The general case was first proved by Ferdinand Frobenius in 1878.
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