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The Maximal and Minimal Ranks of Some Expressions of Generalized Inverses of Matrices

  • Original Article
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Southeast Asian Bulletin of Mathematics

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−.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Queen’s University Kingston, Ontario, K7L 3N6, Canada

    Yongge Tian

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  1. Yongge Tian
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Correspondence to Yongge Tian.

Additional information

The research of the author was supported in part by the Natural Sciences and Engineering Research Council of Canada.

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Cite this article

Tian, Y. The Maximal and Minimal Ranks of Some Expressions of Generalized Inverses of Matrices. SEA bull. math. 25, 745–755 (2002). https://doi.org/10.1007/s100120200015

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  • DOI: https://doi.org/10.1007/s100120200015

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