Sign patterns of J-orthogonal matrices

Frank J. Hall, et al. "Sign patterns of J-orthogonal matrices." Special Matrices 5.1 (2017): 225-241. <http://eudml.org/doc/288285>.

@article{FrankJ2017,
abstract = {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.},
author = {Frank J. Hall, Zhongshan Li, Caroline T. Parnass, Miroslav Rozložník},
journal = {Special Matrices},
keywords = {G-matrix; J-orthogonal matrix; Sign pattern matrix; Sign patterns that allow J-orthogonality},
language = {eng},
number = {1},
pages = {225-241},
title = {Sign patterns of J-orthogonal matrices},
url = {http://eudml.org/doc/288285},
volume = {5},
year = {2017},
}

TY - JOUR
AU - Frank J. Hall
AU - Zhongshan Li
AU - Caroline T. Parnass
AU - Miroslav Rozložník
TI - Sign patterns of J-orthogonal matrices
JO - Special Matrices
PY - 2017
VL - 5
IS - 1
SP - 225
EP - 241
AB - 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.
LA - eng
KW - G-matrix; J-orthogonal matrix; Sign pattern matrix; Sign patterns that allow J-orthogonality
UR - http://eudml.org/doc/288285
ER -