Using the cayleyhamilton theorem to solve linear systems. We compute the characteristic polynomial and apply the cayleyhamilton theorem for the inverse. This document contains a proof of the cayleyhamilton theorem based on the development of matrices in holmultivariate analysis. A proof of the cayley hamilton theorem chris bernhardt let mn. Then in that region fs may be expressed as a polynomial fs x1 k0. Written for the course mathematics 4101 at brooklyn college of cuny. Using ch theorem and a system of equations 6 example. The cayleyhamilton theorem cht is a classic result in linear algebra over fields which states that a matrix satisfies its own characteristic polynomial. Computing the matrix exponential the cayleyhamilton method. Let a be a square matrix of dimension n, with characteristic polynomial. As an application, we show that any polynomial in a can be represented as linear combination of a and the identity matrix i. Find the inverse matrix using the cayleyhamilton theorem.
In linear algebra, when studying a particular matrix, one is often interested in polynomial relations satisfied by this matrix. In linear algebra, cayley hamilton theorem says that. This result is true for any square matrix with entries in a commutative ring. An inductive proof of the cayleyhamilton theorem unt. We state and prove the cayleyhamilton theorem for a 2x2 matrix a. Home university of southern california dissertations and theses using the cayleyhamilton theorem to solve linear systems of difference equations. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext.
Description in this article, the author investigates a computational proof of the cayleyhamilton theroem, based on induction. We verify the cayleyhamilton theorem for the real 3x3 matrix a. Please subscribe the chanel for more vedios and please su. The cayley hamilton theorem asserts that if one substitutes a for. Mathematical methods for engineers and scientists 1, 2, dan 3 k. An n matrix a satisfies its characteristic equation. How to find characteristics equation of any matrix. An important detail is the identity matrix i multiplying the ad cb term so all the terms are matrices.