# Sign patterns of J-orthogonal matrices

Frank J. Hall; Zhongshan Li; Caroline T. Parnass; Miroslav Rozložník

Special Matrices (2017)

- Volume: 5, Issue: 1, page 225-241
- ISSN: 2300-7451

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topFrank 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 -

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