Abstract
In this paper, necessary and sufficient conditions are presented for reducibility of the ternary forms associated to 3×3 unitary bordering matrices. A one-parameter family of n×n unitary bordering matrices is given for which its associated ternary form is the product of linear and quadratic forms for n≤6. As a consequence, the higher rank numerical ranges of this family of unitary bordering matrices have elliptical boundaries.
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