Higher numerical ranges of quaternion matrices

Abstract

Let n and k be two positive integers and k n. In this paper, the notion of kânumerical range of nâsquare quaternion matrices is introduced. Some algebraic and geometrical properties are investigated. In particular, a necessary and sufficient condition for the convexity of the kânumerical range of a quaternion matrix is given. Moreover, a new description of 1ânumerical range of normal quaternion matrices is also stated.