Nonsingularity of the difference and the sum of two idempotent matrices |
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Authors: | Kezheng Zuo |
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Affiliation: | Math Department, Hubei Normal University, Hubei, Huangshi 435002, China |
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Abstract: | Groß and Trenkler 1 pointed out that if a difference of idempotent matrices P and Q is nonsingular, then so is their sum, and Koliha et al2 expressed explicitly a condition, which combined with the nonsingularity of P+Q ensures the nonsingularity of P-Q. In the present paper, these results are strengthened by showing that the nonsingularity of P-Q is in fact equivalent to the nonsingularity of any combination aP+bQ-cPQ (where a≠0,b≠0,a+b=c), and the nonsingularity of P+Q is equivalent to the nonsingularity of any combination aP+bQ-cPQ (where a≠0,b≠0,a+b≠c). |
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Keywords: | 15A03 15A24 |
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