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A note on the generalized rank reduction

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Abstract

We give constructive necessary and sufficient conditions for the validity of the generalized rank reduction formula of Ouellette [12]:

$$ r(A - AN(M^T AN)^ - M^T A) = r(A) - r(AM(M^T AN)^ - M^T ). $$

We also analyze the sufficient conditions of Takane and Yanai [16] showing that some of them are also necessary.

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Author notes

  1. A. Galántai

    Present address: John von Neumann Faculty of Informatics, Budapest Tech, Bécsi út 96/b, 1034, Budapest, Hungary

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  1. University of Miskolc, 3515, Miskolc, Hungary

    A. Galántai

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  1. A. Galántai
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Galántai, A. A note on the generalized rank reduction. Acta Math Hung 116, 239–246 (2007). https://doi.org/10.1007/s10474-007-6038-1

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  • DOI: https://doi.org/10.1007/s10474-007-6038-1

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