The group inverse of the combinations of two idempotent matrices |
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| Authors: | Xiaoji Liu Lingling Wu Yaoming Yu |
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| Affiliation: | 1. College of Mathematics and Computer Science, Guangxi University for Nationalities , Nanning 530006, P.R. China xiaojiliu72@yahoo.com.cn;3. College of Mathematics and Computer Science, Guangxi University for Nationalities , Nanning 530006, P.R. China;4. School of Mathematical Sciences , Building 28, Monash University, VIC 3800, Australia |
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| Abstract: | In this article, we discuss the group inverse of aP + bQ + cPQ + dQP + ePQP + fQPQ + gPQPQ of idempotent matrices P and Q, where a, b, c, d, e, f, g ∈ ? and a ≠ 0, b ≠ 0, put forward its explicit expressions, and some necessary and sufficient conditions for the existence of the group inverse of aP + bQ + cPQ. |
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| Keywords: | group inverse idempotent matrix linear combination |
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