Journal of Mathematical Sciences

, Volume 207, Issue 5, pp 767–775 | Cite as

Some Characterizations of Nekrasov and S-Nekrasov Matrices


It is known that the Nekrasov and S-Nekrasov matrices form subclasses of (nonsingular) H-matrices. The paper presents some necessary and sufficient conditions for a square matrix with complex entries to be a Nekrasov and an S-Nekrasov matrix. In particular, characterizations of the Nekrasov and S-Nekrasov matrices in terms of the diagonal column scaling matrices transforming them into strictly diagonally dominant matrices are obtained. Bibliography: 15 titles.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press (1979).Google Scholar
  2. 2.
    L. Cvetković, V. Kostić, M. Kovačević, and T. Szulc, “Further results on H-matrices and their Schur complements,” Appl. Math. Comput., 198, 506–510 (2008).CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    L. Cvetković, V. Kostić, and S. Rauški, “A new subclass of H-matrices,” Appl. Math. Comput., 208, 206–210 (2009).CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    L. Cvetković, V. Kostić, and R. S. Varga, “A new Geršgorin-type eigenvalue inclusion set,” ETNA, 18, 73–80 (2004).MATHGoogle Scholar
  5. 5.
    L. Cvetković and M. Nedović, “Special H-matrices and their Schur and diagonal-Schur complements,” Appl. Math. Comput., 208, 225–230 (2009).CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Y. M. Gao and X. H. Wang, “Criteria for generalized diagonally dominant and M -matrices,” Linear Algebra Appl., 169, 257–268 (1992).CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    V. V. Gudkov, “On a criterion of matrices non-singularity,” in: Latv. Math. Yearbook [in Russian], Riga (1966), pp. 385–390.Google Scholar
  8. 8.
    L. Yu. Kolotilina, “Pseudoblock conditions of diagonal dominance,” Zap. Nauchn. Semin. POMI, 323, 94–131 (2005).MATHGoogle Scholar
  9. 9.
    L. Yu. Kolotilina, “Bounds for the determinants and inverses of certain H-matrices,” Zap. Nauchn. Semin. POMI, 346, 81–102 (2007).Google Scholar
  10. 10.
    L. Yu. Kolotilina, “Improving Chistyakov’s bounds for the Perron root of a nonnegative matrix,” Zap. Nauchn. Semin. POMI, 346, 103–118 (2007).Google Scholar
  11. 11.
    L. Yu. Kolotilina, “Bounds for the infinity norm of the inverse for certain M - and H -matrices,” Linear Algebra Appl., 430, 692–702 (2009).CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    L. Yu. Kolotilina, “Diagonal dominance characterization of PM- and PH-matrices,” Zap. Nauchn Semin. POMI, 367, 110–120 (2009).Google Scholar
  13. 13.
    A. Ostrowski, “¨Uber die Determinanten mit überwiegender Hauptdiagonale,” Comment. Math. Helv., 10, 69–96 (1937).CrossRefMathSciNetGoogle Scholar
  14. 14.
    F. Robert, “Blocs-H-matrices et convergence des méthodes itérative,” Linear Algebra Appl., 2, 223–265 (1969).CrossRefMATHGoogle Scholar
  15. 15.
    R. S. Varga, Geršgorin and His Circles, Springer (2004). 775Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.St.Petersburg Department of the Steklov Mathematical InstituteSt.PetersburgRussia

Personalised recommendations