Higher numerical ranges of quaternion matrices

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Narjes Haj Aboutalebi
Gholamreza Aghamollaei
Hossein Momenaee Kermani


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.

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