Cayley–Hamilton theorem
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. The characteristic polynomial of an n × n {\displaystyle n\times n} matrix A is defined as p A ( λ ) = det ( λ I n − A ) {\displaystyle p_{A}(\lambda )=\det(\lambda I_{n}-A)} , where det is the determinant operation, λ is a variable scalar element of the base ring, and In is the n × n {\displaystyle n\times n} identity matrix.