Higher rank numerical ranges of rectangular matrix polynomials
Subject Areas : Linear and multilinear algebra; matrix theory
Gh. Aghamollaei
1
(Department of Mathematics, Shahid Bahonar University of Kerman, 76169-14111, Kerman, Iran)
M. Zahraei
2
(Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran)
Keywords: isometry, numerical range, Rank-k numerical range, rectangular matrix polynomials,
Abstract :
In this paper, the notion of rank-k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated.Moreover, for ϵ > 0; the notion of Birkhoff-James approximate orthogonality sets for ϵ-higherrank numerical ranges of rectangular matrix polynomials is also introduced and studied. The proposed denitions yield a natural generalization of the standard higher rank numericalranges.