Cayley hamilton theorem: Learn the proof and

Learn the proof and applications of the Cayley-Hamilton theorem, which states that the characteristic polynomial of a matrix vanishes at that matrix. See how to decompose the kernel of the characteristic polynomial into generalized eigenspaces using polynomials that are relatively prime. 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. 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. In linear algebra, the Cayley–Hamilton theorem (termed after the mathematicians Arthur Cayley and William Rowan Hamilton) says that every square matrix over a commutative ring (for instance the real or complex field) satisfies its own characteristic equation.