This paper builds upon the results in the article “G-matrices, J-orthogonal matrices, and their sign patterns", Czechoslovak Math. J. 66 (2016), 653-670, by Hall and Rozloznik. A number of further general results on the sign patterns of the J-orthogonal matrices are proved. Properties of block diagonal matrices and their sign patterns are examined. It is shown that all 4 × 4 full sign patterns allow J-orthogonality. Important tools in this analysis are Theorem 2.2 on the exchange operator and Theorem 3.2 on the characterization of J-orthogonal matrices in the paper “J-orthogonal matrices: properties and generation", SIAM Review 45 (3) (2003), 504-519, by Higham. As a result, it follows that for n ≤4 all n×n full sign patterns allow a J-orthogonal matrix as well as a G-matrix. In addition, the 3 × 3 sign patterns of the J-orthogonal matrices which have zero entries are characterized.
@article{bwmeta1.element.doi-10_1515_spma-2017-0016,
author = {Frank J. Hall and Zhongshan Li and Caroline T. Parnass and Miroslav Rozlo\v zn\'\i k},
title = {Sign patterns of J-orthogonal matrices},
journal = {Special Matrices},
volume = {5},
year = {2017},
pages = {225-241},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_spma-2017-0016}
}
Frank J. Hall; Zhongshan Li; Caroline T. Parnass; Miroslav Rozložník. Sign patterns of J-orthogonal matrices. Special Matrices, Tome 5 (2017) pp. 225-241. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_spma-2017-0016/