Baksalary, Jerzy K.; Baksalary, Oskar Maria On linear combinations of generalized projectors. (English) Zbl 1081.15016 Linear Algebra Appl. 388, 17-24 (2004). 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. Reviewer: Omar Hirzallah (Zarqa) Cited in 1 ReviewCited in 10 Documents MSC: 15B57 Hermitian, skew-Hermitian, and related matrices 15A27 Commutativity of matrices Keywords:idempotent matrix; quadripotent matrix; partial isometry; projector; orthogonal projector PDF BibTeX XML Cite \textit{J. K. Baksalary} and \textit{O. M. Baksalary}, Linear Algebra Appl. 388, 17--24 (2004; Zbl 1081.15016) Full Text: DOI OpenURL 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.