## Idempotency of linear combinations of an idempotent matrix and a tripotent matrix.(English)Zbl 1016.15027

Let $$A$$ be a matrix with entries in the complex numbers. Then $$A$$ is called idempotent if $$A^2=A$$, it is called tripotent if $$A^3=A.$$ If $$B_1$$ and $$B_2$$ are nonzero idempotent matrices, then $$B=B_1-B_2$$ is called essentially tripotent.
Suppose $$A$$ is idempotent, $$B$$ is essentially tripotent, and $$c_1,c_2\neq 0.$$ The authors determine when a linear combination $$c_1A+c_2B$$ is idempotent.

### MSC:

 15B57 Hermitian, skew-Hermitian, and related matrices 62H10 Multivariate distribution of statistics 15A63 Quadratic and bilinear forms, inner products
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### References:

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