Baksalary, Jerzy K.; Baksalary, Oskar Maria Nonsingularity of linear combinations of idempotent matrices. (English) Zbl 1081.15017 Linear Algebra Appl. 388, 25-29 (2004). The authors show that, for idempotent \(n\times n\) complex matrices \(P_1\) and \(P_2\), the nonsingularity of \(P_1+P_2\) is equivalent to the nonsingularity of \(c_1P_1+c_2P_2\), where \(c_1\) and \(c_2\) are nonzero complex numbers satisfying \(c_1+c_2\neq0\). Reviewer: Omar Hirzallah (Zarqa) Cited in 2 ReviewsCited in 23 Documents MSC: 15B57 Hermitian, skew-Hermitian, and related matrices 15A24 Matrix equations and identities 15A09 Theory of matrix inversion and generalized inverses Keywords:oblique projector; difference of projectors; sum of projectors; linear combination of projectors PDF BibTeX XML Cite \textit{J. K. Baksalary} and \textit{O. M. Baksalary}, Linear Algebra Appl. 388, 25--29 (2004; Zbl 1081.15017) Full Text: DOI OpenURL References: [1] Groß, J; Trenkler, G, Nonsingularity of the difference of two oblique projectors, SIAM J. matrix anal. appl., 21, 390-395, (1999) · Zbl 0946.15020 [2] J.J. Koliha, V. Rakočević, I. Straškraba, The difference and sum of projectors, Linear Algebra Appl., in press (doi:10.1016/j.laa.2004.03.008) 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.