Sign patterns of J-orthogonal matrices

• Autorzy: Frank J. Hall , Zhongshan Li , Caroline T. Parnass , Miroslav Rozložník
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

G-matrix; J-orthogonal matrix; Sign pattern matrix; Sign patterns that allow J-orthogonality

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2017
• Tom: 5
• Numer: 1
• Strony: 225-241

Daty

wydano

2017-10-26

otrzymano

2017-07-27

zaakceptowano

2017-09-20

online

2017-10-28

Twórcy

autor

Frank J. Hall

• , GA 30303,

autor

Zhongshan Li

• , GA 30303,

autor

Caroline T. Parnass

• , GA 30303,

autor

Miroslav Rozložník

• 1,

Identyfikatory

DOI

10.1515/spma-2017-0016