Date of Award
Master of Science (MS)
Mathematics and Statistics
This thesis builds upon the results in “G-matrices, J-orthogonal matrices, and their sign patterns”, Czechoslovak Math. J. 66 (2016), 653-670, by Hall and Rozloˇzn ́ık. Some general results about the sign patterns of J-orthogonal matrices are proved, including about block diagonal matrices. It is shown that every full 4 × 4 sign pattern allows J -orthogonality and as a result that, for n ≤ 4, all n × n full sign patterns allow a J-orthogonal matrix as well as a G-matrix. The 3 × 3 sign patterns of the J -orthogonal matrices which have zero entires are also characterized.
Parnass, Caroline, "Sign Patterns of J-orthogonal Matrices." Thesis, Georgia State University, 2017.