## Nonsingularity of linear combinations of idempotent matrices.(English)Zbl 1081.15017

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 $$c_1+c_2\neq0$$.

### MSC:

 15B57 Hermitian, skew-Hermitian, and related matrices 15A24 Matrix equations and identities 15A09 Theory of matrix inversion and generalized inverses
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### 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)
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