276
Views
23
CrossRef citations to date
0
Altmetric
Original Articles

The Cauchy interlacing theorem in simple Euclidean Jordan algebras and some consequences

&
Pages 65-86 | Received 23 Aug 2008, Accepted 15 Sep 2009, Published online: 20 Apr 2010

References

  • Baes , M . 2007 . Convexity and differentiability properties of spectral functions and spectral mappings on Euclidean Jordan algebras . Linear Algebra Appl. , 422 : 664 – 700 .
  • Bapat , RB and Raghavan , TES . 1997 . Nonnegative Matrices and Applications , Cambridge : Cambridge University Press .
  • Bauschke , HH , Güler , O , Lewis , AS and Sendev , HS . June 1998 . Hyperbolic Polynomials and Convex Analysis, Research Report, CORR 98-29 , June , Department of Combinatorics and Optimization, University of Waterloo .
  • Bhatia , R . 1997 . Matrix Analysis , New York : Springer Graduate Texts in Mathematics, Springer-Verlag .
  • Dray , T and Manogue , CA . 1998 . The octonionic eigenvalue problem . Adv. Appl. Clifford Alg. , 8 : 341 – 364 .
  • Fan , K and Pall , G . 1957 . Imbedding conditions for Hermitian and normal matrices . Canad. J. Math. , 9 : 298 – 304 .
  • Faraut , J and Korányi , A . 1994 . Analysis on Symmetric Cones , Oxford : Clarendon Press .
  • Faybusovich , L . 2006 . Jordan-algebraic approach to convexity theorems for quadratic mappings . SIAM J. Optim. , 17 : 558 – 576 .
  • Gowda , MS and Sznajder , R . 2006 . Automorphism invariance of P- and GUS-properties of linear transformations on Euclidean Jordan algebras . Math. Oper. Res. , 31 : 109 – 123 .
  • Gowda , MS , Sznajder , R and Tao , J . 2004 . Some P-properties for linear transformations on Euclidean Jordan algebras . Linear Algebra Appl. , 393 : 203 – 232 .
  • Gowda , MS , Tao , J and Moldovan , M . 2009 . Some inertia theorems in Euclidean Jordan algebras . Linear Algebra Appl. , 430 : 1992 – 2011 .
  • Hardy , GH , Littlewood , JE and Polya , G . 1952 . Inequalities , Cambridge, , UK : Cambridge University Press .
  • Hirzebruch , U . 1970 . Der min–max-satz von E. Fischer für formal-reelle Jordan-algebren . Math. Ann. , 186 : 65 – 69 .
  • Horn , RA and Johnson , CR . 1985 . Matrix Analysis , Cambridge : Cambridge University Press .
  • Lim , Y , Kim , J and Faybusovich , L . 2003 . Simultaneous diagonalization on simple Euclidean Jordan algebras and its applications . Forum Math. , 15 : 639 – 644 .
  • Mirsky , L . 1975 . A trace inequality of John von Neumann . Monatsh. Math. , 79 : 303 – 306 .
  • Moldovan , MM and Gowda , MS . 2009 . Strict diagonal dominance and a Gersgorin type theorem in Euclidean Jordan algebras . Linear Alg. Appl. , 431 : 148 – 161 .
  • Ostrowski , A and Schneider , H . 1962 . Some theorems on the inertia of general matrices . J. Math. Anal. Appl. , 4 : 72 – 84 .
  • Schmieta , SH and Alizadeh , F . 2003 . Extension of primal-dual interior point algorithms to symmetric cones . Math. Prog., Series A , 96 : 409 – 438 .
  • Tam , TY . 1999 . Interlacing inequalities and Cartan subspaces of classical real simple Lie algebras . SIAM J. Matrix Anal. Appl. , 21 : 581 – 592 .
  • Tao , J . 2004 . Some P-properties for linear transformations on the Lorentz cone, PhD Thesis , University of Maryland, Baltimore County .
  • Theobald , CM . 1975 . An inequality for the trace of the product of two symmetric matrices . Math. Proc. Cambridge Phil. Soc. , 77 : 265 – 267 .
  • Tian , Y . 2000 . Matrix representations of octonions and their applications . Adv. Appl. Clifford Alg. , 10 : 61 – 90 .
  • Wimmer , HK . 1973 . On the Ostrowski–Schneider inertia theorem . J. Math. Anal. Appl. , 41 : 164 – 169 .

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.