## On linear combinations of two tripotent, idempotent, and involutive matrices.(English)Zbl 1165.15022

Let (1) $$A = c_{1}A_{1} + c_{2}A_{2}$$, where $$c_{1}, c_{2}$$ are nonzero complex numbers, and ($$A_1, A_2$$) is a pair of two $$n\times n$$ nonzero matrices. The purpose of this paper is mainly twofold: in case $$A_1$$ and $$A_2$$ are involutive matrices, to characterize all situations where a linear combination of the form (1) is a tripotent or an idempotent or an involutive matrix, then to determine all situations where a linear combination of the form (1) is an involutive matrix when $$A_1$$ and $$A_2$$ are tripotent or idempotent matrices.

### MSC:

 15B57 Hermitian, skew-Hermitian, and related matrices
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### References:

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