Sign patterns of J-orthogonal matrices

0480731 - MÚ 2018 RIV PL eng J - Článek v odborném periodiku
Hall, F.J. - Li, Z. - Parnass, C. - Rozložník, Miroslav
Sign patterns of J-orthogonal matrices.
Special Matrices. Roč. 5, č. 1 (2017), s. 225-241. ISSN 2300-7451
Institucionální podpora: RVO:67985840
Klíčová slova: G-matrix * J-orthogonal matrix * sign pattern matrix * sign patterns that allow J-orthogonality
Obor OECD: Applied mathematics
https://www.degruyter.com/view/j/spma.2017.5.issue-1/spma-2017-0016/spma-2017-0016.xml?format=INT

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.
Trvalý link: http://hdl.handle.net/11104/0276431