In this paper, a new characterization of previously studied generalized complementary basic matrices is obtained. It is in terms of ranks and structure ranks of submatrices defined by certain diagonal positions. The results concern both the irreducible and general cases.
@article{bwmeta1.element.doi-10_2478_spma-2014-0013,
author = {Miroslav Fiedler and Frank J. Hall},
title = {A new characterization of generalized complementary basic matrices},
journal = {Special Matrices},
volume = {2},
year = {2014},
zbl = {1310.15003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_spma-2014-0013}
}
Miroslav Fiedler; Frank J. Hall. A new characterization of generalized complementary basic matrices. Special Matrices, Tome 2 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_spma-2014-0013/
[1] M. Fiedler, Structure ranks of matrices, Linear Algebra Appl. 179 (1993), 119–128. | Zbl 0766.15003
[2] M. Fiedler, Complementary basic matrices, Linear Algebra Appl. 384 (2004), 199–206. | Zbl 1059.15026
[3] M. Fiedler and F. J. Hall, G-matrices, Linear Algebra Appl. 436 (2012), 731–741.
[4] M. Fiedler and F. J. Hall, A note on permanents and generalized complementary basic matrices, Linear Algebra Appl. 436 (2012), 3553–3569. [WoS] | Zbl 1241.15005
[5] M. Fiedler and F. J. Hall, Some graph theoretic properties of generalized complementary basic matrices, Linear Algebra Appl. 438 (2013), 3365–3374. [WoS] | Zbl 1261.05055
[6] M. Fiedler and F. J. Hall, Factorizable matrices, Special Matrices. 1 (2013), 3–9. | Zbl 1291.15033