Geometric proof of some theorems of Schur-Horn type

Linear Algebra and Its Applications

Volumn 286, Issue 1-3, 1999, Pages 149-173

  Leite, R S ^a   Richa, T R W ^a   Tomei, C ^a  

^a PONTIFICAL CATHOLIC UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

Moment map; Schur Horn theorem

Indexed keywords

EID: 0039035755     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(98)10169-6     Document Type: Article

References (16)

1. A. Horn, Doubly stochastic matrices and the diagonal of a rotation matrix, Amer. J. Math. 76 (1954) 620-630.
2. A.W. Marshall, I. Olkin, Inequalities: theory of majorization and its applications, Mathematics in Science and Engineering, vol. 143, Academic Press, New York, 1979.
3. I. Schur, Über eine klasse von mittelbindungen mit anwendungen auf der determinanten theorie, S.B. Berlin Math. Ges. 22 (1923) 9-20.
4. B. Kostant, On convexity, the Weyl group and the Iwasawa decomposition, Ann. Sci. École Norm. Sup. 6 (4) (1973) 413-455.
5. M. Atiyah, Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14 (1982) 1-15.
6. V. Guillemin, S. Sternberg, Convexity properties of the moment mapping I, Inv. Math. 67 (1982) 491-513.
7. J. Duistermaat, The momentum maps, collection topics in differential geometry, vol. I and II, Colloq. Math. Soc. Janos Bolyal 46 (1988) 347-392.
8. R.S. Leite, Uma demonstração geométrica do teorema de Schur-Horn, Master thesis, Depto. de Matemática, PUC-Rio, Rio de Janeiro, 1996.
9. N. MacKey, personal communication.
10. V. Guillemin, A. Pollack, Differential Topology, Prentice Hall, Englewood Cliffs, NJ, 1974.
11. R. Bott, Non-degenerate critical manifolds, Ann. Math. 60 (1954) 248-261.
12. M. Spivak, A Comprehensive Introduction to Differential Geometry, vol. V, Publish or Perish Inc., Boston, MA, 1979.
13. J. Humphreys, Reflection groups and Coxeter groups, Cambridge Studies in Advanced Mathematics, vol. 29, Cambridge University Press, Cambridge, 1990.
14. R. Abraham, J. Marsden, Foundations of Mechanics, Benjamin/Cummings, Reading, MA, 1978.
15. P. Lax, Integrals of nonlinear equations of evolution and solitary waves, Comm. Pure Appl. Math. 21 (1968) 467-490.
16. G. Hardy, J. Littlewood, G. Polya, Inequalities, Cambridge University Press, Cambridge, 1952.