Some results on higher numerical ranges and radii of quaternion matrices

Subject Areas : History and biography

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

Received: 2015-12-20 Accepted : 2016-03-11 Published : 2015-12-01

Keywords: &lrm, $k-$numerical radius&lrm, , &lrm, right $k$-spectral radius&lrm, , &lrm, $k$-norm&lrm, , &lrm, quaternion matrices,

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.

References:

[1] N. Haj Aboutalebi, Gh. Aghamollaei and H. Momenaee Kermani, Higher numerical ranges of quaternion matrices, Electronic J. Linear Algebra, 30 (2015), 889-904.

[2] R. Kippenhahn, Uber die Wertvorrat einer Matrix, Math. Nachr. 6 (1951), 193-228.

[3] C.K. Li, T.Y. Tam and N.K. Tsing, The generalized spectral radius, numerical radius and spectral norm, Linear Multilinear Algebra, 16 (1984), 215-237.

[4] F. Zhang, Quaternions and matrices of quaternions, Linear Algebra Appl. 251 (1997), 21-57.