A new aspect of Hankel matrices via Krylov matrix

作者：Cheon Gi Sang^*; Kim Hana

来源：Linear Algebra and Its Applications, 2013, 438(1): 361-373.

DOI：10.1016/j.laa.2012.07.040

• Hankel matrix
• Krylov matrix
• Companion matrix
• Compatible matrix

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 C-T. Firstly we focus on algebraic structures of Krylov matrices of C over a field IF. We then discuss an equivalent condition for the Hankel matrix to be a Krylov matrix of C-T 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.

• 出版日期2013-1-1