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Keywords

Quaternion matrices, k-numerical range, numerical range

Abstract

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.

abs_vol30_pp889-904.pdf (25 kB)
Abstract

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