Quaternionic numerical range is not always a convex set. In this note, an explicit criterion is given for the convexity of quaternionic numerical range.

MSC Classifications:

15A33, 15A60 show english descriptions Matrices over special rings (quaternions, finite fields, etc.)
Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05] 15A33 - Matrices over special rings (quaternions, finite fields, etc.)
15A60 - Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05]

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