Perron-Frobenius theory on the higher-rank numerical range for some classes of real matrices

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Hormozgan, Bandar Abbas, Iran

2 Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.

Abstract

We present an extension of Perron-Frobenius theory to the higher-rank numerical range
of real matrices. We define a new type of the rank-k numerical radius for real matrices, i.e., the
sign-real rank-k numerical radius‎, and derive some properties of it. In addition, we extend Issos' results on the higher-rank numerical range of nonnegative matrices to real matrices.‎
Finally, we give some examples that are used to illustrate our theoretical results.‎‎

Keywords


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Volume 10, Issue 2
Special Issue Dedicated to Professor M. Radjabalipour on the occasion of his 75th birthday.
October 2021
Pages 49-61
  • Receive Date: 11 May 2021
  • Revise Date: 29 July 2021
  • Accept Date: 05 August 2021