Optimality of the trace of a product of matrices
DOI:
https://doi.org/10.22199/S07160917.1999.0001.00005Keywords:
Trace inequality, Singular valuesAbstract
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.
References
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[2] R. W. Brockett, Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems, Linear Algebra Appl., 146, pp. 79-91, (1991).
[3] R. W. Brockett, Differential geometry and the design of gradient algorithms, Proceedings of Symposia in Pure Mathematics, 54 (1993), pp. 69-92.
[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, pp.
760- 766, (1951).
[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), pp.
125-134.
[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
of Combinatorics and Optimization, University of Waterloo, (1995).
[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,
(1975).
[12] J. von Neumann, Some matrix inequalities and metrization of matrix
space, Tomsk. Univ. Rev. 1, pp. 286 - 300, (1937). Collected Works,
Vol 4, Pergamon, Oxford, pp. 205- 219, (1962).
Published
2018-04-04
How to Cite
[1]
H. Miranda P., “Optimality of the trace of a product of matrices”, Proyecciones (Antofagasta, On line), vol. 18, no. 1, pp. 71-76, Apr. 2018.
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