131
Views
2
CrossRef citations to date
0
Altmetric
Articles

On the boundary of rank-k numerical ranges

Pages 1266-1271 | Received 19 Feb 2013, Accepted 27 Jun 2013, Published online: 06 Sep 2013

References

  • Gustafson KE, Rao DKM. Numerical range: the field of values of linear operators and matrices. New York: Springer; 1996.
  • Halmos PR. A Hilbert problem book. New York: Springer; 1982.
  • Horn RA, Johnson CR. Topics in matrix analysis. Cambridge: Cambridge Univ. Press; 1991.
  • Chien MT, Nakazato H. Elliptic curves arising from numerical ranges. Int. J. Pure Appl. Math. 2006;30:441–465.
  • Gau HL, Wu PY. Condition for the numerical range to contain an elliptic disc. Linear Algebra Appl. 2003;364:213–222.
  • Gau HL, Wu PY. Line segments and elliptic arcs on the boundary of a numerical range. Linear Multilinear Algebra. 2008;56:131–142.
  • Keeler D, Rodman L, Spitkovsky I. The numerical range of 3 x 3 matrices. Linear Algebra Appl. 1997;252:115–139.
  • Wu PY. Numerical ranges as circular discs. Appl. Math. Lett. 2011;24:2115–2117.
  • Cheung WS, Li CK. Elementary proofs for some results on the circular symmetry of the numerical range. Linear Multilinear Algebra. 2013;61:596–602.
  • Choi MD, Kribs D, Życzkowski K. Quantum error correcting codes from the compression formalism. Rep. Math. Phys. 2006;58:77–86.
  • Choi MD, Kribs D, Życzkowski K. Higher rank numerical ranges and compression problems. Linear Algebra Appl. 2006;418:828–839.
  • Woerdeman H. The higher rank numerical range is convex. Linear Multilinear Algebra. 2008;56:65–67.
  • Li CK, Sze NS. Canonical forms, higher rank numerical ranges, totally isotropic subspaces, and matrix equations. Proc. Amer. Math. Soc. 2008;136:3013–3023.
  • Li CK, Poon YT, Sze NS. Elliptical range theorems for generalized numerical ranges of quadratic operators. Rocky Mount. J. Math. 2011;41:813–832.
  • Chien MT, Nakazato H. The boundary of higher rank numerical ranges. Linear Algebra Appl. 2011;435:2971–2985.
  • Rellich F. Perturbation theory of eigenvalues problems. Notes on mathematics and its applications. New York: Taylor Francis; 1969.
  • Baumgärtel H. Analytic perturbtaion theory for matrices and operators. Operator Theory. Berlin: Birkhäuser Verlag; 1985.
  • Joswig M, Straub B. On the numerical range map. J. Austral. Math. Soc. 1998;65:267–283.
  • Leake T, Lins B, Spitovky IM. Pre-images of boundary points of the numerical ranges, submitted for publication.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.