Higher rank numerical ranges of rectangular matrix polynomials

الموضوعات :

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)

تاريخ الإرسال : 29 الإثنين , ذو الحجة, 1436 تاريخ التأكيد : 17 الإثنين , ربيع الأول, 1437 تاريخ الإصدار : 08 الثلاثاء , ربيع الأول, 1436

الکلمات المفتاحية: isometry, numerical range, Rank-k numerical range, rectangular matrix polynomials,

ملخص المقالة :

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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