Teorema de cayley hamilton para matrices pdf

Introduction hyper matrices appear in several contexts in mathematics 22, 23, 24 and in. Cayleyhamilton theorem for 2x2 matrices cosmolearning. Computing the matrix exponential the cayley hamilton method 1 the matrix exponential eat forms the basis for the homogeneous unforced and the forced response of lti systems. This is a somewhat highbrow way of showing the cayley hamilton theorem, through the power of holomorphic functional calculus. Versione del 2 maggio 2011 argomenti scelti sulla triangolazione di matrici, il teorema di cayley hamilton e sulla forma. In linear algebra, the cayleyhamilton 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 typical equation. As an application, we show that any polynomial in a can be represented as linear combination of a and the identity matrix i. As i mentioned in this answer, one of the standard ways to define a matrix function is through a cauchylike construction. Cayley hamilton theorem a square matrix satisfies its own characteristic equation. The cayley hamilton theorem is an immediate consequence of the existence of the jordan normal form for matrices over algebraically closed fields. Given a square matrix a and writing i for the identity matrix of the same size, the characteristic polynomial of a is the determinant of the matrix. Consider a square matrix a with dimension n and with a characteristic polynomial. We make some remarks regarding a direct proof of cayley hamilton theorem. In the case of a 3 3 matrix we present such a direct proof.