Higher rank numerical ranges of rectangular matrix polynomials

محورهای موضوعی : 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)

تاریخ دریافت : 1394/07/20 تاریخ پذیرش : 1394/10/07 تاریخ انتشار : 1393/10/09

کلید واژه: isometry, numerical range, Rank-k numerical range, rectangular matrix polynomials,

چکیده مقاله :

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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