Article ID Journal Published Year Pages File Type
6416729 Linear Algebra and its Applications 2013 13 Pages PDF
Abstract

An investigation is made of the Krylov matrices associated to the companion matrix C of a monic polynomial p(x) of degree n. In this paper, we propose a new approach to the study of Hankel matrices as Krylov matrices of CT. Firstly we focus on algebraic structures of Krylov matrices of C over a field F. We then discuss an equivalent condition for the Hankel matrix to be a Krylov matrix of CT by the notion of compatibility. As a result, we derive new determinant formulas for such Hankel matrices in terms of eigenvalues and eigenvectors of C respectively.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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