Canonical forms, higher rank numerical ranges, totally isotropic subspaces, and matrix equations

Chi Kwong Li, Nung Sing Sze

Research output: Journal article publicationJournal articleAcademic researchpeer-review

53 Citations (Scopus)

Abstract

The results on matrix canonical forms are used to give a complete description of the higher rank numerical range of matrices arising from the study of quantum error correction. It is shown that the set can be obtained as the intersection of closed half planes (of complex numbers). As a result, it is always a convex set in ℂ. Moreover, the higher rank numerical range of a normal matrix is a convex polygon determined by the eigenvalues. These two consequences confirm the conjectures of Choi et al. on the subject. In addition, the results are used to derive a formula for the optimal upper bound for the dimension of a totally isotropic subspace of a square matrix and to verify the solvability of certain matrix equations.
Original languageEnglish
Pages (from-to)3013-3023
Number of pages11
JournalProceedings of the American Mathematical Society
Volume136
Issue number9
DOIs
Publication statusPublished - 1 Sep 2008
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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