On higher rank numerical hulls of normal matrices

Document Type: Research Paper

Authors

1 Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Islamic Republic of Iran

2 Department of Mathematics, Payame Noor University (PNU) ;Tehran; Islamic Republic of Iran.

10.22072/wala.2017.47123.1080

Abstract

‎In this paper‎, ‎some algebraic and geometrical properties of the rank$-k$ numerical hulls of normal matrices are investigated‎. ‎A characterization of normal matrices whose rank$-1$ numerical hulls are equal to their numerical range is given‎. ‎Moreover‎, ‎using the extreme points of the numerical range‎, ‎the higher rank numerical hulls of matrices of the form $A_1 \oplus i A_2$‎, ‎where $A_1$ and $A_2$ are Hermitian‎, ‎are investigated‎. ‎The higher rank numerical hulls of the basic circulant matrix‎ ‎are also studied‎.

Keywords


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