The Maximal and Minimal Ranks of Some Expressions of Generalized Inverses of Matrices |
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Authors: | Yongge Tian |
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Institution: | (1) Department of Mathematics and Statistics, Queens University Kingston, Ontario, K7L 3N6, Canada |
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Abstract: | In this paper, we first determine the maximal and minimal ranks of A — BXC with respect to X. Using those results, we then find the maximal and minimal ranks of the expressions AA– — A– A — BB– A — AC– C and B– BA — ACC– with respect to the choice of generalized inverses A–, B– and C–. In particular, we consider the commutativity of A and A–, Ak and A–.The research of the author was supported in part by the Natural Sciences and Engineering Research Council of Canada. |
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Keywords: | generalized inverse idempotent matrix rank equality maximal and minimal ranks |
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