Combinatorial aspects of generalized complementary basic matrices

Miroslav Fiedler; Frank Hall

Open Mathematics (2013)

  • Volume: 11, Issue: 12, page 2186-2196
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Miroslav Fiedler, and Frank Hall. "Combinatorial aspects of generalized complementary basic matrices." Open Mathematics 11.12 (2013): 2186-2196. <http://eudml.org/doc/269418>.

@article{MiroslavFiedler2013,
abstract = {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.},
author = {Miroslav Fiedler, Frank Hall},
journal = {Open Mathematics},
keywords = {Factorization; CB-matrix; GCB-matrix; Inheritance properties; P-matrix; Alternating sign matrices; Spectral radius; Sign pattern matrix; factorization; -matrix; spectral radius; sign pattern matrix; generalized complementary basic matrices; alternating sign matrices},
language = {eng},
number = {12},
pages = {2186-2196},
title = {Combinatorial aspects of generalized complementary basic matrices},
url = {http://eudml.org/doc/269418},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Miroslav Fiedler
AU - Frank Hall
TI - Combinatorial aspects of generalized complementary basic matrices
JO - Open Mathematics
PY - 2013
VL - 11
IS - 12
SP - 2186
EP - 2196
AB - 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.
LA - eng
KW - Factorization; CB-matrix; GCB-matrix; Inheritance properties; P-matrix; Alternating sign matrices; Spectral radius; Sign pattern matrix; factorization; -matrix; spectral radius; sign pattern matrix; generalized complementary basic matrices; alternating sign matrices
UR - http://eudml.org/doc/269418
ER -

References

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  13. [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. [14] Horn R.A., Johnson C.R., Matrix Analysis, 2nd ed., Cambridge University Press, Cambridge, 2013 Zbl1267.15001
  15. [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. [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 Zbl0516.05016
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