English

Unitary equivalence to a complex symmetric matrix: low dimensions

Functional Analysis 2012-09-04 v4 Operator Algebras

Abstract

A matrix T\Mn(\C)T \in \M_n(\C) is \emph{UECSM} if it is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. We develop several techniques for studying this property in dimensions three and four. Among other things, we completely characterize 4×44 \times 4 nilpotent matrices which are UECSM and we settle an open problem which has lingered in the 3×33 \times 3 case. We conclude with a discussion concerning a crucial difference which makes dimension three so different from dimensions four and above

Keywords

Cite

@article{arxiv.1104.4960,
  title  = {Unitary equivalence to a complex symmetric matrix: low dimensions},
  author = {Stephan Ramon Garcia and Daniel E. Poore and James E. Tener},
  journal= {arXiv preprint arXiv:1104.4960},
  year   = {2012}
}

Comments

15 pages. To appear in Lin. Alg. Appl

R2 v1 2026-06-21T17:58:54.425Z