## On linear combinations of generalized projectors.(English)Zbl 1081.15016

An $$n\times n$$ complex matrix $$G$$ is called a generalized projector if $$G^2=G^*$$, where $$G^*$$ denotes the conjugate transpose of $$G$$.
The authors establish a complete solution to the problem of when a linear combination of two different generalized projectors is also a generalized projector.

### MSC:

 15B57 Hermitian, skew-Hermitian, and related matrices 15A27 Commutativity of matrices
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### References:

 [1] Baksalary, J.K; Baksalary, O.M, Idempotency of linear combinations of two idempotent matrices, Linear algebra appl., 321, 3-7, (2000) · Zbl 0984.15021 [2] Groß, J; Trenkler, G, Generalized and hypergeneralized projectors, Linear algebra appl., 264, 463-474, (1997) · Zbl 0887.15024 [3] Halmos, P.R, Finite-dimensional vector spaces, (1958), Van Nostrand Princeton · Zbl 0107.01404
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