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.
@article{bwmeta1.element.doi-10_2478_s11533-013-0309-6,
author = {Miroslav Fiedler and Frank Hall},
title = {Combinatorial aspects of generalized complementary basic matrices},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {2186-2196},
zbl = {1288.15038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0309-6}
}
Miroslav Fiedler; Frank Hall. Combinatorial aspects of generalized complementary basic matrices. Open Mathematics, Tome 11 (2013) pp. 2186-2196. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0309-6/
[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 | Zbl 1281.15034
[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 | Zbl 0833.15002
[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 | Zbl 0185.07803
[5] Fiedler M., Complementary basic matrices, Linear Algebra Appl., 2004, 384, 199–206 http://dx.doi.org/10.1016/j.laa.2004.01.014 | Zbl 1059.15026
[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 | Zbl 1135.15009
[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 | Zbl 1254.15020
[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 | Zbl 1241.15005
[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 | Zbl 1261.05055
[11] Fiedler M., Hall F.J., Stroev M., Permanents, determinants, and generalized complementary basic matrices (manuscript) | Zbl 1314.15007
[12] Gantmacher F.R., The Theory of Matrices II, Chelsea, New York, 1959 | Zbl 0085.01001
[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 | Zbl 1267.15001
[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 | Zbl 0516.05016
[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