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Volumn 42, Issue 5, 2000, Pages 813-820

Convex analysis on Cartan subspaces

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FUNCTIONS; OPTIMIZATION; POLES AND ZEROS; SET THEORY; THEOREM PROVING; VECTORS;

EID: 0343878206     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(99)00126-1     Document Type: Article
Times cited : (35)

References (36)
  • 1
    • 0011336089 scopus 로고
    • On the geometry of the unit ball of unitary matrix spaces
    • J. Arazy, On the geometry of the unit ball of unitary matrix spaces, Integral Equations Operator Theory 4 (1981) 151-171.
    • (1981) Integral Equations Operator Theory , vol.4 , pp. 151-171
    • Arazy, J.1
  • 2
    • 84874962985 scopus 로고
    • Convexity and commuting Hamiltonians
    • M.F. Atiyah, Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14 (1982) 1-15.
    • (1982) Bull. London Math. Soc. , vol.14 , pp. 1-15
    • Atiyah, M.F.1
  • 3
    • 0038982701 scopus 로고
    • On the different notions of convexity for rotationally invariant functions
    • B. Dacorogna, H. Koshigoe, On the different notions of convexity for rotationally invariant functions, Ann. Fac. Sci. Toulouse 2 (1993) 163-184.
    • (1993) Ann. Fac. Sci. Toulouse , vol.2 , pp. 163-184
    • Dacorogna, B.1    Koshigoe, H.2
  • 4
    • 0011376467 scopus 로고
    • All convex invariant functions of hermitian matrices
    • C. Davis, All convex invariant functions of hermitian matrices, Arch. Math. 8 (1957) 276-278.
    • (1957) Arch. Math. , vol.8 , pp. 276-278
    • Davis, C.1
  • 5
    • 0000206664 scopus 로고
    • Doubly stochastic matrices and the diagonal of a rotation matrix
    • R.A. Horn, Doubly stochastic matrices and the diagonal of a rotation matrix, Amer. J. Math. 76 (1954) 620-630.
    • (1954) Amer. J. Math. , vol.76 , pp. 620-630
    • Horn, R.A.1
  • 6
    • 0011364748 scopus 로고
    • Exposed faces and duality for symmetric and unitarily invariant norms
    • E.M. de Sa, Exposed faces and duality for symmetric and unitarily invariant norms, Linear Algebra Appl. 197,198 (1994) 429-450.
    • (1994) Linear Algebra Appl. , vol.197-198 , pp. 429-450
    • De Sa, E.M.1
  • 7
    • 43949152335 scopus 로고
    • Faces and traces of the unit ball of a symmetric gauge function
    • E.M. de Sa, Faces and traces of the unit ball of a symmetric gauge function, Linear Algebra Appl. 197,198 (1994) 349-395.
    • (1994) Linear Algebra Appl. , vol.197-198 , pp. 349-395
    • De Sa, E.M.1
  • 8
    • 0040304729 scopus 로고
    • Faces of the unit ball of a unitarily invariant norm
    • E.M. de Sa, Faces of the unit ball of a unitarily invariant norm, Linear Algebra Appl. 197,198 (1994) 451-493.
    • (1994) Linear Algebra Appl. , vol.197-198 , pp. 451-493
    • De Sa, E.M.1
  • 9
    • 0001623641 scopus 로고
    • Reflection groups, generalized Schur functions, and the geometry of majorization
    • M.L. Eaton, M.D. Perlman, Reflection groups, generalized Schur functions, and the geometry of majorization, Ann. Probab. 5 (1977) 829-860.
    • (1977) Ann. Probab. , vol.5 , pp. 829-860
    • Eaton, M.L.1    Perlman, M.D.2
  • 10
    • 84974307372 scopus 로고
    • Some convexity theorems for matrices
    • P.A. Fillmore, J.P. Williams, Some convexity theorems for matrices, Glasgow Math. J. 12 (1971) 110-117.
    • (1971) Glasgow Math. J. , vol.12 , pp. 110-117
    • Fillmore, P.A.1    Williams, J.P.2
  • 12
    • 0000567544 scopus 로고
    • Convexity properties of the moment mapping
    • V. Guillemin, S. Sternberg, Convexity properties of the moment mapping, Invent. Math. 67 (1982) 491-513.
    • (1982) Invent. Math. , vol.67 , pp. 491-513
    • Guillemin, V.1    Sternberg, S.2
  • 13
    • 0001009017 scopus 로고
    • Convexity properties of the moment mapping II
    • V. Guillemin, S. Sternberg, Convexity properties of the moment mapping II, Invent. Math. 77 (1984) 533-546.
    • (1984) Invent. Math. , vol.77 , pp. 533-546
    • Guillemin, V.1    Sternberg, S.2
  • 15
    • 0004151494 scopus 로고
    • Cambridge University Press, Cambridge, UK
    • R.A. Horn, C. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1985.
    • (1985) Matrix Analysis
    • Horn, R.A.1    Johnson, C.2
  • 16
    • 0001009018 scopus 로고
    • Convexity properties of the moment mapping, III
    • F. Kirwan, Convexity properties of the moment mapping, III, Invent. Math. 77 (1984) 547-552.
    • (1984) Invent. Math. , vol.77 , pp. 547-552
    • Kirwan, F.1
  • 17
    • 0000368974 scopus 로고
    • On convexity, the Weyl group and the Iwasawa decomposition
    • B. Kostant, On convexity, the Weyl group and the Iwasawa decomposition, Ann. Sci. l'Ecole Norm. Sup. 6 (1973) 413-455.
    • (1973) Ann. Sci. L'Ecole Norm. Sup. , vol.6 , pp. 413-455
    • Kostant, B.1
  • 18
    • 0039231550 scopus 로고
    • Von Neumann's lemma and a Chevalley-type theorem for convex functions on Cartan subspaces
    • University of Waterloo
    • A.S. Lewis, Von Neumann's lemma and a Chevalley-type theorem for convex functions on Cartan subspaces, Technical Report CORR 95-19, University of Waterloo, 1995.
    • (1995) Technical Report CORR 95-19
    • Lewis, A.S.1
  • 19
    • 0030304775 scopus 로고    scopus 로고
    • Convex analysis on the Hermitian matrices
    • A.S. Lewis, Convex analysis on the Hermitian matrices, SIAM J. Optim. 6 (1996) 164-177.
    • (1996) SIAM J. Optim. , vol.6 , pp. 164-177
    • Lewis, A.S.1
  • 20
    • 0030518228 scopus 로고    scopus 로고
    • Group invariance and convex matrix analysis
    • A.S. Lewis, Group invariance and convex matrix analysis, SIAM J. Matrix Anal. Appl. 17 (1996) 927-949.
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , pp. 927-949
    • Lewis, A.S.1
  • 22
    • 0042208950 scopus 로고    scopus 로고
    • Group majorization and Schur type inequalities
    • M. Niezgoda, Group majorization and Schur type inequalities, Linear Algebra Appl. 268 (1998) 9-30.
    • (1998) Linear Algebra Appl. , vol.268 , pp. 9-30
    • Niezgoda, M.1
  • 24
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, NJ
    • R.T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 25
    • 0002679616 scopus 로고
    • Uber eine Klasse von Mittelbildungen mit Anwendungen auf der Determinantentheorie
    • I. Schur, Uber eine Klasse von Mittelbildungen mit Anwendungen auf der Determinantentheorie, Sitzungsber. Berliner Math. Gesellschaft 22 (1923) 9-20.
    • (1923) Sitzungsber. Berliner Math. Gesellschaft , vol.22 , pp. 9-20
    • Schur, I.1
  • 26
    • 38249019585 scopus 로고
    • G-majorization, group-induced cone orderings and reflection groups
    • A.G.M. Steerneman, G-majorization, group-induced cone orderings and reflection groups, Linear Algebra Appl. 127 (1990) 107-119.
    • (1990) Linear Algebra Appl. , vol.127 , pp. 107-119
    • Steerneman, A.G.M.1
  • 27
    • 33646084429 scopus 로고    scopus 로고
    • An extension of a result of Lewis
    • Auburn University
    • B.T.-Y. Tam, An extension of a result of Lewis, Technical report, Auburn University, 1998.
    • (1998) Technical Report
    • Tam, B.T.-Y.1
  • 29
    • 0030106462 scopus 로고    scopus 로고
    • Semidefinite programming
    • L. Vandenberghe, S. Boyd, Semidefinite programming, SIAM Rev. 38 (1996) 49-95.
    • (1996) SIAM Rev. , vol.38 , pp. 49-95
    • Vandenberghe, L.1    Boyd, S.2
  • 30
    • 33646114808 scopus 로고    scopus 로고
    • Une note sur les fonctions invariantes
    • F. Vincent, Une note sur les fonctions invariantes, Ann. Fac. Sci. Toulouse 6 (1997) 357-363.
    • (1997) Ann. Fac. Sci. Toulouse , vol.6 , pp. 357-363
    • Vincent, F.1
  • 31
    • 0000011340 scopus 로고
    • Some matrix inequalities and metrization of matric-space
    • J. von Neumann, Some matrix inequalities and metrization of matric-space, Tomsk Univ. Rev. 1 (1937) 286-300.
    • (1937) Tomsk Univ. Rev. , vol.1 , pp. 286-300
    • Von Neumann, J.1
  • 32
    • 0011328006 scopus 로고
    • Pergamon, Oxford
    • In: Collected Works, Pergamon, Oxford, 1962, vol. IV, pp. 205-218.
    • (1962) Collected Works , vol.4 , pp. 205-218
  • 33
    • 0011336092 scopus 로고
    • Characterization of the subdifferential of some matrix norms
    • G.A. Watson, Characterization of the subdifferential of some matrix norms, Linear Algebra Appl. 170 (1992) 33-45.
    • (1992) Linear Algebra Appl. , vol.170 , pp. 33-45
    • Watson, G.A.1
  • 34
    • 0011284872 scopus 로고
    • On matrix approximation problems with Ky Fan k norms
    • G.A. Watson, On matrix approximation problems with Ky Fan k norms, Numer. Algorithms 5 (1993) 263-272.
    • (1993) Numer. Algorithms , vol.5 , pp. 263-272
    • Watson, G.A.1
  • 35
    • 33747712347 scopus 로고
    • On the characterization of the extremal points of the unit sphere of matrices
    • K. Ziȩtak, On the characterization of the extremal points of the unit sphere of matrices, Linear Algebra Appl. 106 (1988) 57-75.
    • (1988) Linear Algebra Appl. , vol.106 , pp. 57-75
    • Ziȩtak, K.1
  • 36
    • 0011375032 scopus 로고
    • Subdifferentials, faces and dual matrices
    • K. Ziȩtak, Subdifferentials, faces and dual matrices, Linear Algebra Appl. 185 (1993) 125-141.
    • (1993) Linear Algebra Appl. , vol.185 , pp. 125-141
    • Ziȩtak, K.1


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