Advanced search
Publication Cover
Linear and Multilinear Algebra Volume 59, 2011 - Issue 10: Quantum Information Science, and Numerical Ranges
Submit an article Journal homepage
159
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

A range associated with skew symmetric matrix

Xuhua Liu Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849-5310, USACorrespondence[email protected]
,
Dawit G. Tadesse Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849-5310, USA
&
Tin-Yau Tam Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849-5310, USA
Pages 1105-1120 | Received 12 Aug 2010, Accepted 02 Sep 2010, Published online: 23 Sep 2011

References

  • Berger , CA . 1963 . Normal dilations , Cornell University : Ph.D. diss. .
  • Brickman , L . 1961 . On the field of values of a matrix . Proc. Am. Math. Soc. , 12 : 61 – 66 .
  • Cheung , W-S , Liu , X and Tam , T-Y . 2011 . Multiplicities, boundary points, and joint numerical ranges . Oper. Matrices. , 5 : 41 – 52 .
  • Davis , C . 1971 . The Toeplitz–Hausdorff theorem explained . Canad. Math. Bull. , 14 : 245 – 246 .
  • Donoghue , WF Jr . 1957 . On the numerical range of a bounded operator, Michigan Math. J. , 4 : 261 – 263 .
  • Embry , MR . 1970 . The numerical range of an operator . Pacific J. Math. , 32 : 647 – 650 .
  • Halmos , PR . 1982 . A Hilbert Space Problem Book , New York : Springer-Verlag .
  • Helgason , S . 1978 . Differential Geometry, Lie Groups, and Symmetric Spaces , New York : Academic Press .
  • Horn , RA and Johnson , CR . 1985 . Matrix Analysis , Cambridge : Cambridge University Press .
  • Horn , RA and Johnson , CR . 1991 . Topics in Matrix Analysis , Cambridge : Cambridge University Press .
  • Johnson , CR . 1976 . Functional characterizations of the field of values and the convex hull of the spectrum . Proc. Am. Math. Soc. , 61 : 201 – 204 .
  • Knapp , AW . 1996 . Lie Groups Beyond an Introduction , Boston : Birkhäuser .
  • Li , CK . 1996 . A simple proof of the elliptical range theorem . Proc. Am. Math. Soc. , 124 : 1985 – 1986 .
  • Li , CK . 1996 . Some convexity theorems for the generalized numerical ranges . Linear Multilinear Alg. , 40 : 235 – 240 .
  • Li , CK and Tam , TY . 2000 . Numerical ranges arising from simple Lie algebras . J. Canad. Math. Soc. , 52 : 141 – 171 .
  • McIntosh , A . 1978 . The Toeplitz–Hausdorff theorem and ellipticity conditions . Am. Math. Monthly , 85 : 475 – 477 .
  • Pearcy , C . 1966 . An elementary proof of the power inequality for the numerical radius . Michigan Math. J. , 13 : 289 – 291 .
  • Stampfli , JG . 1966 . Extreme points of the numerical range of hyponormal operators . Michigan Math. J. , 13 : 87 – 89 .
  • Stillwell , J . 2008 . Naive Lie Theory , New York : Springer .
  • Tam , TY . 1999 . An extension of a convexity theorem of the generalized numerical range associated with SO(2n + 1) . Proc. Am. Math. Soc. , 127 : 35 – 44 .
  • Tam , TY . 2002 . Convexity of generalized numerical range associated with a compact Lie group . J. Aust. Math. Soc. , 72 : 57 – 66 .
  • Tsing , NK . 1984 . The constrained bilinear form and the C-numerical range . Linear Alg. Appl. , 56 : 195 – 206 .
  • Warner , FW . 1971 . Foundation of Differentiable Manifolds and Lie Groups , Glenview, IL : Scott Foresman and Company .

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:

Order Reprints Request Corporate Permissions

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:

Request Academic Permissions

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.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.