Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
Abstract
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.
Aghamollaei, G., & Nourollahi, M. A. (2015). Higher numerical ranges of matrix polynomials. Bulletin of the Iranian Mathematical Society, 41(Issue 7 (Special Issue)), 29-45.
MLA
Aghamollaei, G., & Nourollahi, M. A. "Higher numerical ranges of matrix polynomials", Bulletin of the Iranian Mathematical Society, 41, Issue 7 (Special Issue), 2015, 29-45.
HARVARD
Aghamollaei G., Nourollahi M. A. (2015). 'Higher numerical ranges of matrix polynomials', Bulletin of the Iranian Mathematical Society, 41(Issue 7 (Special Issue)), pp. 29-45.
CHICAGO
G. Aghamollaei & M. A. Nourollahi, "Higher numerical ranges of matrix polynomials," Bulletin of the Iranian Mathematical Society, 41 Issue 7 (Special Issue) (2015): 29-45,
VANCOUVER
Aghamollaei G., Nourollahi M. A. Higher numerical ranges of matrix polynomials. BIMS. 2015;41(Issue 7 (Special Issue)):29-45.
