Optimality of the trace of a product of matrices

• Miranda P., Héctor ^[1]
  1. [1] Universidad de Bío Bío.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 18, Nº. 1, 1999, págs. 71-76
• Idioma: inglés
• DOI: 10.22199/S07160917.1999.0001.00005
• Enlaces
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• Resumen

  • A simple and short proof of the optimality conditions in the John von Neumann trace inequality for singular values is shown. Possible generalizations and special cases are also considered.

• Referencias bibliográficas
  • Citas [1] J. M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rat. Mech. Anal., 63, pp. 337- 403, (1977).
  • [2] R. W. Brockett, Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems, Linear Algebra Appl.,...
  • [3] R. W. Brockett, Differential geometry and the design of gradient algorithms, Proceedings of Symposia in Pure Mathematics, 54 (1993), pp....
  • [4] P. G. Ciarlet, Mathematical Elasticity, Vol. I, North-Holland, Amsterdam, (1988).
  • [5] E. M. de Sá, Exposed faces and duality for symmetric and unitarily invariant narms, Linear Algebra Appl., 197/198, pp. 429-450, (1994).
  • [6] K. Fan, Maximum properties and inequalities far the eigenvalues af campletely continuaus aperatars, Proc. Nat. Acad. Sci. U.S.A., 37,...
  • [7] S. Friedland, Inverse eigenvalue problems, Linear Algebra Appl., 17, pp. 15- 51, (1977).
  • [8] H. A. L. Kiers and J. M. F. Ten Berge, Optimality canditians far the trace af certain matrix products, Linear Algebra Appl., 126 (1989),...
  • [9] W. Kristof, A thearem an the trace af certain matrix products and same applicatians, J. Math. Psych., 7, pp. 515- 530, (1970).
  • [10] A. S. Lewis, Van Neumann's lemma and a Chevalley-type thearem far convex functians an Cartan subspaces, Research Report, Department...
  • [11] C. M. Theobald, An inequality far the trace af the product af twa symmetric matrices, Math. Proc. Camb. Phil. Soc., 77, pp. 265- 267,...
  • [12] J. von Neumann, Some matrix inequalities and metrization of matrix space, Tomsk. Univ. Rev. 1, pp. 286 - 300, (1937). Collected Works,...