G-matrices, J-orthogonal matrices, and their sign patterns

Title:

G-matrices, J-orthogonal matrices, and their sign patterns

Creator:

Hall, Frank J and Miroslav Rozložník

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:87e847b7-96f0-470e-b2f4-346ff5606cfe
uuid:87e847b7-96f0-470e-b2f4-346ff5606cfe
issn:0011-4642

Subject:

Matematika, matematika, mathematics, G-matrix, J-orthogonal matrix, Cauchy matrix, sign pattern matrix, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

A real matrix A is a G-matrix if A is nonsingular and there exist nonsingular diagonal matrices D_{1} and D_{2} such that A^{-T} = D_{1}AD_{2}, where A^{-T} denotes the transpose of the inverse of A. Denote by J = diag(±1) a diagonal (signature) matrix, each of whose diagonal entries is +1 or −1. A nonsingular real matrix Q is called J-orthogonal if Q^{T} JQ = J. Many connections are established between these matrices. In particular, a matrix A is a G-matrix if and only if A is diagonally (with positive diagonals) equivalent to a column permutation of a J-orthogonal matrix. An investigation into the sign patterns of the J-orthogonal matrices is initiated. It is observed that the sign patterns of the G-matrices are exactly the column permutations of the sign patterns of the J-orthogonal matrices. Some interesting constructions of certain J-orthogonal matrices are exhibited. It is shown that every symmetric staircase sign pattern matrix allows a J-orthogonal matrix. Sign potentially J-orthogonal conditions are also considered. Some examples and open questions are provided., Frank J. Hall, Miroslav Rozložník., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Source:

Czechoslovak Mathematical Journal | 2016 Volume:66 | Number:3

Harvested from:

CDK

Metadata only:

false