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BY-NC-ND 4.0 license Open Access Published by De Gruyter Open Access October 28, 2017

Sign patterns of J-orthogonal matrices

  • Frank J. Hall EMAIL logo , Zhongshan Li , Caroline T. Parnass and Miroslav Rozložník
From the journal Special Matrices

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.

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Received: 2017-07-27
Accepted: 2017-09-20
Published Online: 2017-10-28
Published in Print: 2017-10-26

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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