Higher numerical ranges of matrix polynomials

Document Type : Research Paper


Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.


 Let $P(\lambda)$ be an $n$-square complex matrix polynomial, and $1 \leq k \leq n$ be a positive integer. In this paper, some algebraic and geometrical properties of the $k$-numerical range of $P(\lambda)$ are investigated. In particular, the relationship between the $k$-numerical range of $P(\lambda)$ and the $k$-numerical range of its companion linearization is stated. Moreover, the $k$-numerical range of the basic $A$-factor block circulant matrix, which is the block companion matrix of the matrix polynomial $P(\lambda) = \lambda ^m I_n - A$, is studied.


Main Subjects

Volume 41, Issue 7 (Special Issue)
December 2015
Pages 29-45
  • Receive Date: 15 October 2014
  • Revise Date: 09 January 2015
  • Accept Date: 11 January 2015
  • First Publish Date: 01 December 2015