Some results on higher numerical ranges and radii of quaternion matrices

Document Type: Research Paper

Authors

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

2 Department of Mathematics, Shahrood Branch, Islamic Azad University, Shahrood, Iran

Abstract

‎Let $n$ and $k$ be two positive integers‎, ‎$k\leq n$ and $A$ be an $n$-square quaternion matrix‎. ‎In this paper‎, ‎some results on the $k-$numerical range of $A$ are investigated‎. ‎Moreover‎, ‎the notions of $k$-numerical radius‎, ‎right $k$-spectral radius and $k$-norm of $A$ are introduced‎, ‎and some of their algebraic properties are studied‎.

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