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Volumn 413, Issue 2-3 SPEC. ISS., 2006, Pages 594-618

Riemannian geometry and matrix geometric means

Author keywords

Geometric mean; Gradient; Positive definite matrix; Riemannian manifold; Semi parallelogram law

Indexed keywords

GEOMETRY; MATHEMATICAL TECHNIQUES; PROBLEM SOLVING;

EID: 31444440896     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2005.08.025     Document Type: Conference Paper
Times cited : (257)

References (13)
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    • T. Ando Concavity of certain maps on positive definite matrices and applications to Hadamard products Linear Algebra Appl. 26 1979 203 241
    • (1979) Linear Algebra Appl. , vol.26 , pp. 203-241
    • Ando, T.1
  • 5
    • 0142094477 scopus 로고    scopus 로고
    • On the exponential metric increasing property
    • R. Bhatia On the exponential metric increasing property Linear Algebra Appl. 375 2003 211 220
    • (2003) Linear Algebra Appl. , vol.375 , pp. 211-220
    • Bhatia, R.1
  • 7
    • 0007460916 scopus 로고
    • Geodesics and operator means in the space of positive operators
    • G. Corach, H. Porta, and L. Recht Geodesics and operator means in the space of positive operators Int. J. Math. 4 1993 193 202
    • (1993) Int. J. Math. , vol.4 , pp. 193-202
    • Corach, G.1    Porta, H.2    Recht, L.3
  • 8
    • 0035601362 scopus 로고    scopus 로고
    • The geometric mean, matrices, metrics, and more
    • J.D. Lawson, and Y. Lim The geometric mean, matrices, metrics, and more Amer. Math. Monthly 108 2001 797 812
    • (2001) Amer. Math. Monthly , vol.108 , pp. 797-812
    • Lawson, J.D.1    Lim, Y.2
  • 9
    • 22944439423 scopus 로고    scopus 로고
    • A differential geometric approach to the geometric mean of symmetric positive-definite matrices
    • M. Moakher A differential geometric approach to the geometric mean of symmetric positive-definite matrices SIAM J. Matrix Anal. Appl. 26 2005 735 747
    • (2005) SIAM J. Matrix Anal. Appl. , vol.26 , pp. 735-747
    • Moakher, M.1
  • 12
    • 0001438007 scopus 로고
    • Functional calculus for sesquilinear forms and the purification map
    • W. Pusz, and S.L. Woronowicz Functional calculus for sesquilinear forms and the purification map Reports Math. Phys. 8 1975 159 170
    • (1975) Reports Math. Phys. , vol.8 , pp. 159-170
    • Pusz, W.1    Woronowicz, S.L.2
  • 13
    • 0013389128 scopus 로고
    • Hermitian semidefinite matrix means and related matrix inequalities-an introduction
    • G.E. Trapp Hermitian semidefinite matrix means and related matrix inequalities-an introduction Linear and Multilinear Algebra 16 1984 113 123
    • (1984) Linear and Multilinear Algebra , vol.16 , pp. 113-123
    • Trapp, G.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.