Quasi-orthogonal subalgebras of 4 × 4 matrices

Hiromichi Ohno, D. Petz, András Szántó

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Maximal Abelian quasi-orthogonal subalgebras form a popular research problem. In this paper quasi-orthogonal subalgebras of M4 (C) isomorphic to M2 (C) are studied. It is proved that if four such subalgebras are given, then their orthogonal complement is always a commutative subalgebra. In particular, five such subalgebras do not exist. A conjecture is made about the maximal number of pairwise quasi-orthogonal subalgebras of M2n (C).

Original languageEnglish
Pages (from-to)109-118
Number of pages10
JournalLinear Algebra and Its Applications
Volume425
Issue number1
DOIs
Publication statusPublished - Aug 1 2007

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Subalgebra
Pairwise
Complement
Isomorphic

Keywords

  • Cartan decomposition
  • Pauli matrices
  • Quasi-orthogonality

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis

Cite this

Quasi-orthogonal subalgebras of 4 × 4 matrices. / Ohno, Hiromichi; Petz, D.; Szántó, András.

In: Linear Algebra and Its Applications, Vol. 425, No. 1, 01.08.2007, p. 109-118.

Research output: Contribution to journalArticle

Ohno, Hiromichi ; Petz, D. ; Szántó, András. / Quasi-orthogonal subalgebras of 4 × 4 matrices. In: Linear Algebra and Its Applications. 2007 ; Vol. 425, No. 1. pp. 109-118.
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