Quaternion matrices, k-numerical range, numerical range
Let n and k be two positive integers and k n. In this paper, the notion of k−numerical range of n−square quaternion matrices is introduced. Some algebraic and geometrical properties are investigated. In particular, a necessary and sufficient condition for the convexity of the k−numerical range of a quaternion matrix is given. Moreover, a new description of 1−numerical range of normal quaternion matrices is also stated.
Haj Aboutalebi, Narjes; Aghamollaei, Gholamreza; and Momenaee Kermani, Hossein.
"Higher numerical ranges of quaternion matrices",
Electronic Journal of Linear Algebra,
Volume 30, pp. 889-904.