Abstract
Let T 1 and T 2 be two nonzero commuting n × n tripotent matrices and c 1 , c 2 two nonzero complex numbers. Necessary and sufficient conditions for the tripotency and the idempotency of c 1 T 1 + c 2 T 2 are obtained. The problems considered here have also statistical importance when c 1 , c 2 are real scalars and T 1 , T 2 are real symmetric matrices.
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