Higher rank numerical ranges of rectangular matrix polynomials

Authors

Gh. Aghamollaei Department of Mathematics, Shahid Bahonar University of Kerman, 76169-14111, Kerman, Iran

M. Zahraei 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 denitions yield a natural generalization of the standard higher rank numerical ranges.

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Journal title

Journal of Linear and Topological Algebra (JLTA)

volume 03 issue 03

pages 173- 184

publication date 2014-12-30

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Keywords

Rank-k numerical range isometry numerical range rectangular matrix polynomials

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