Abstract
This paper is a continuation of the article ‘Topological properties of J-orthogonal matrices’, Linear and Multilinear Algebra 66(2018), 2524–2533, by the authors. Let be the set of all
real matrices. A matrix
is said to be a signature matrix if J is diagonal and its diagonal entries are
. If J is a signature matrix, a nonsingular matrix
is said to be a J-orthogonal matrix if
. Let
be the set of all
, J-orthogonal matrices. In this paper some further interesting properties of these matrices are obtained. In particular, an open question stated in the preceding article about
is answered. Proposition 3.2 on the characterization of J-orthogonal matrices in the paper ‘J-orthogonal matrices: properties and generation’, SIAM Review 45(2003), 504–519, by N. J. Higham is again heavily used. The standard linear operators
that strongly preserve J-orthogonal matrices, i.e.
is J-orthogonal if and only if A is J-orthogonal are characterized.
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Acknowledgments
The authors thank Professor Michael Stewart of Georgia State University for the elegant proof of Lemma 2.8. Also they thank the referee for very good suggestions.
Disclosure statement
No potential conflict of interest was reported by the authors.