Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6416729 | Linear Algebra and its Applications | 2013 | 13 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Gi-Sang Cheon, Hana Kim,