authors
- Borobia, Alberto
- Canogar, Roberto
- TERAN VERGARA, FERNANDO DE
On the consistency of the matrix equation XT AX=B when B is symmetric: the case where CFC(A) includes skew-symmetric blocks
Articles
Overview
published in
publication date
- January 2023
issue
- 61 (2023)
volume
- 117
Digital Object Identifier (DOI)
International Standard Serial Number (ISSN)
- 1578-7303
Electronic International Standard Serial Number (EISSN)
- 1579-1505
abstract
- In this paper, which is a follow-up to Borobia et al. (Mediterr J Math, 18:40, 2021), we provide a necessary and sufficient condition for the matrix equation XT AX=B to be consistent when B is symmetric. The condition depends on the canonical form for congruence of the matrix A, and is proved to be necessary for all matrices A, and sufficient for most of them. This result improves the main one in the previous paper, since the condition is stronger than the one in that reference, and the sufficiency is guaranteed for a larger set of matrices (namely, those whose canonical form for congruence, CFC(A), includes skew-symmetric blocks).