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Nonsingularity of the difference and the sum of two idempotent matrices. (English) Zbl 1195.15005
It is shown that for any two idempotent matrices $P, Q$ the nonsingularity of $P-Q$ is equivalent to the nonsingularity of any combination $aP+bQ-cPQ$ ($a, b\ne 0, \ a+b=c$), and the nonsingularity of $P+Q$ is equivalent to the nonsingularity of any combination $aP+bQ-cPQ$ ($a, b\ne 0,\ a+b\ne c$).

MSC:
15A09Matrix inversion, generalized inverses
15A03Vector spaces, linear dependence, rank
15A24Matrix equations and identities
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References:
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