Higher rank numerical ranges of rectangular matrix polynomials

Authors

1 Department of Mathematics, Shahid Bahonar University of Kerman, 76169-14111, Kerman, Iran

2 Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran

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-higher rank numerical ranges of rectangular matrix polynomials is also introduced and studied. The
proposed de nitions yield a natural generalization of the standard higher rank numerical ranges.

Keywords

Main Subjects


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