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On the Generic Rank of Matrices Composed of Kronecker Products

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Abstract

In the present paper we study the generic ranks of special matrix-valued maps defined by certain systems of parameters via Kronecker products. We introduce the notions of minimal superabundant, balanced and reducible systems. The main result of the paper is a theorem for maps with minimal superabundant systems of parameters. For such systems it associates the value of the generic rank with the balancedness. The proof of this theorem is based on a reduction by the parameters and consists of verifying the fact of reducibility.

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References

  1. Sh. Friedland, Linear Algebra Appl. 436 (3), 478–497 (2012).

    Article  MathSciNet  Google Scholar 

  2. V. Strassen, Linear Algebra Appl. 52, 645–685 (1983).

    Article  MathSciNet  Google Scholar 

  3. Th. Lickteig, Linear Algebra Appl. 69, 95–120 (1985).

    Article  MathSciNet  Google Scholar 

  4. G. Abo, G. Ottaviani, and C. Peterson, Trans. Am. Math. Soc. 361 (2), 767–792 (2009).

    Article  Google Scholar 

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Authors and Affiliations

  1. Moscow State University, Moscow, 119991, Russia

    D. A. Stefonishin

  2. Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow, 119333, Russia

    D. A. Stefonishin

Authors
  1. D. A. Stefonishin
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Correspondence to D. A. Stefonishin.

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Original Russian Text © D.A. Stefonishin, 2018, published in Doklady Akademii Nauk, 2018, Vol. 479, No. 2, pp. 130–133.

The article was translated by the author.

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Stefonishin, D.A. On the Generic Rank of Matrices Composed of Kronecker Products. Dokl. Math. 97, 125–128 (2018). https://doi.org/10.1134/S1064562418020060

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  • DOI: https://doi.org/10.1134/S1064562418020060

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