Some results on higher numerical ranges and radii of quaternion matrices
الموضوعات :Gh. Aghamollaei 1 , N. Haj Aboutalebi 2
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
الکلمات المفتاحية: &lrm, $k-$numerical radius&lrm, , &lrm, right $k$-spectral radius&lrm, , &lrm, $k$-norm&lrm, , &lrm, quaternion matrices,
ملخص المقالة :
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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[4] F. Zhang, Quaternions and matrices of quaternions, Linear Algebra Appl. 251 (1997), 21-57.
