The cayley hamilton theorem is an immediate consequence of the existence of the jordan normal form for matrices over algebraically closed fields. We consider here a method of determining eat based on the the cayley hamiton theorem. As i mentioned in this answer, one of the standard ways to define a matrix function is through a cauchylike construction. Finding matrix functions is a common occurrence in modern day research. Introduction hyper matrices appear in several contexts in mathematics 22, 23, 24 and in. We state and prove the cayley hamilton theorem for a 2x2 matrix a. Adil aslam linear algebra 1 p a g e my email address is. 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. Teorema di cayley hamilton, forma canonica e triangolazioni. Cayleyhamilton theorem for 2x2 matrices cosmolearning. Consider a square matrix a with dimension n and with a characteristic polynomial.
Cayley hamilton theorem a square matrix satisfies its own characteristic equation. We make some remarks regarding a direct proof of cayley hamilton theorem. A, which is a polynomial of the cayley hamilton theorem asserts that if one substitutes a for. 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. 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. Teorema di cayleyhamilton, forma canonica e triangolazioni. Versione del 2 maggio 2011 argomenti scelti sulla triangolazione di matrici, il teorema di cayley hamilton e sulla forma. In the case of a 3 3 matrix we present such a direct proof. Computing the matrix exponential the cayleyhamilton method.