Cayley–Hamilton theorem
Square matrices satisfy their characteristic equation
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. Since each entry of the matrix...
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