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)

Received: 2015-10-12 Accepted : 2015-12-28 Published : 2014-12-30

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 denitions yield a natural generalization of the standard higher rank numericalranges.

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