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2013 | 11 | 12 | 2186-2196
Tytuł artykułu

Combinatorial aspects of generalized complementary basic matrices

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper extends some properties of the generalized complementary basic matrices, in particular, in a combinatorial direction. These include inheritance (such as for Alternating Sign Matrices), spectral, and sign pattern matrix (including sign nonsingularity) properties.
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
12
Strony
2186-2196
Opis fizyczny
Daty
wydano
2013-12-01
online
2013-10-08
Twórcy
autor
Bibliografia
  • [1] Brualdi R.A., Kiernan K.P., Meyer S.A., Schroeder M.W., Patterns of alternating sign matrices, Linear Algebra Appl., 2013, 438(10), 3967–3990 http://dx.doi.org/10.1016/j.laa.2012.03.009
  • [2] Brualdi R.A., Ryser H.J., Combinatorial Matrix Theory, Encyclopedia Math. Appl., 39, Cambridge University Press, Cambridge, 1991 http://dx.doi.org/10.1017/CBO9781107325708
  • [3] Brualdi R.A., Shader B.L., Matrices of Sign-Solvable Linear Systems, Cambridge Tracts in Math., 116, Cambridge University Press, Cambridge, 1995 http://dx.doi.org/10.1017/CBO9780511574733
  • [4] Chow T.S., A class of Hessenberg matrices with known eigenvalues and inverses, SIAM Rev., 1969, 11(3), 391–395 http://dx.doi.org/10.1137/1011065
  • [5] Fiedler M., Complementary basic matrices, Linear Algebra Appl., 2004, 384, 199–206 http://dx.doi.org/10.1016/j.laa.2004.01.014
  • [6] Fiedler M., Intrinsic products and factorizations of matrices, Linear Algebra Appl., 2008, 428(1), 5–13 http://dx.doi.org/10.1016/j.laa.2007.09.026
  • [7] Fiedler M., Hall F.J., Some inheritance properties for complementary basic matrices, Linear Algebra Appl., 2010, 433(11–12), 2060–2069 http://dx.doi.org/10.1016/j.laa.2010.07.017
  • [8] Fiedler M., Hall F.J., G-matrices, Linear Algebra Appl., 2012, 436(3), 731–741 http://dx.doi.org/10.1016/j.laa.2011.08.001
  • [9] Fiedler M., Hall F.J., A note on permanents and generalized complementary basic matrices, Linear Algebra Appl., 2012, 436(9), 3553–3569 http://dx.doi.org/10.1016/j.laa.2011.12.030
  • [10] Fiedler M., Hall F.J., Some graph theoretic properties of generalized complementary basic matrices, Linear Algebra Appl., 2013, 438(8), 3365–3374 http://dx.doi.org/10.1016/j.laa.2012.12.028
  • [11] Fiedler M., Hall F.J., Stroev M., Permanents, determinants, and generalized complementary basic matrices (manuscript)
  • [12] Gantmacher F.R., The Theory of Matrices II, Chelsea, New York, 1959
  • [13] Hall F.J., Li Z., Sign Pattern Matrices, In: Handbook of Linear Algebra, Discrete Math. Appl. (Boca Raton), Chapman & Hall/CRC, Boca Raton, 2007
  • [14] Horn R.A., Johnson C.R., Matrix Analysis, 2nd ed., Cambridge University Press, Cambridge, 2013
  • [15] Johnson C.R., Sign patterns of inverse nonnegative matrices, Linear Algebra Appl., 1983, 55, 69–80 http://dx.doi.org/10.1016/0024-3795(83)90166-0
  • [16] Mills W.H., Robbins D.P., Rumsey H. Jr., Alternating-sign matrices and descending plane partitions, J. Combin. Theory Ser. A, 1983, 34(3), 340–359 http://dx.doi.org/10.1016/0097-3165(83)90068-7
  • [17] Seymour P.D., Decomposition of regular matroids, J. Comb. Theory Ser. B, 1980, 28(3), 305–359 http://dx.doi.org/10.1016/0095-8956(80)90075-1
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0309-6
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