Cayley hamilton theorem: The Cayley-Hamilton theorem produces an explicit polynomial

The Cayley-Hamilton theorem produces an explicit polynomial relation satisfied by a given matrix. In particular, if M M is a matrix and p M (x) = det (M x I) pM (x) = det(M − xI) is its characteristic polynomial, the Cayley-Hamilton theorem states that p M (M) = 0 pM (M) = 0. Learn the Cayley Hamilton Theorem with a clear statement, step-by-step proof, essential formulas, and solved examples. Understand how matrices satisfy their own characteristic equations. Problems of the Cayley-Hamilton Theorem. From introductory exercise problems to linear algebra exam problems from various universities. Basic to advanced level. Cayley-Hamilton theorem by Marco Taboga, PhD The Cayley-Hamilton theorem shows that the characteristic polynomial of a square matrix is identically equal to zero when it is transformed into a polynomial in the matrix itself. In other words, a square matrix satisfies its own characteristic equation.