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.


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