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Volumn 32, Issue , 2005, Pages 129-139

Means of positive matrices: Geometry and a conjecture

Author keywords

Geometric mean; Information geometry; Logarithmic mean; Operator means; Positive matrices

Indexed keywords


EID: 34547871974     PISSN: 17875021     EISSN: 17876117     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (15)

References (14)
  • 4
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    • The logarithmic mean
    • Carlson, B. C., The logarithmic mean, Amer. Math. Monthly, Vol. 79 (1972), 615–618.
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    • Carlson, B.C.1
  • 5
    • 0036376868 scopus 로고    scopus 로고
    • Gauss-composition of means and the solution of the Matkowski-Sutő problem
    • Daróczy, Z., Páles, Zs., Gauss-composition of means and the solution of the Matkowski-Sutő problem, Publ. Math. Debrecen, 61(2002), 157–218.
    • (2002) Publ. Math. Debrecen , vol.61 , pp. 157-218
    • Daróczy, Z.1    Páles, Z.2
  • 6
    • 0037098552 scopus 로고    scopus 로고
    • Invariant means
    • Horwitz, A., Invariant means, J. Math. Anal. Appl., Vol. 270 (2002), 499–518.
    • (2002) J. Math. Anal. Appl. , vol.270 , pp. 499-518
    • Horwitz, A.1
  • 7
    • 0000472839 scopus 로고
    • Means of positive linear operators
    • Kubo, F., Ando, T., Means of positive linear operators, Math. Ann., Vol. 246 (1980), 205–224.
    • (1980) Math. Ann. , vol.246 , pp. 205-224
    • Kubo, F.1    Ando, T.2
  • 8
    • 0034346424 scopus 로고    scopus 로고
    • Geometric means of symmetric connes
    • Lim, Y., Geometric means of symmetric connes, Arch. Math., Vol. 75 (2000), 39–45.
    • (2000) Arch. Math. , vol.75 , pp. 39-45
    • Lim, Y.1
  • 9
    • 22944439423 scopus 로고    scopus 로고
    • A differential geometric approach to the geometric mean of symmetric positive definite matrices
    • Moakher, M., A differential geometric approach to the geometric mean of symmetric positive definite matrices, SIAM J. Matrix Anal. Appl., Vol. 26 (2005), 735–747.
    • (2005) SIAM J. Matrix Anal. Appl. , vol.26 , pp. 735-747
    • Moakher, M.1
  • 10
    • 0030508084 scopus 로고    scopus 로고
    • Dualistic differential geometry of positive definite matrices and its applications to related problems
    • Ohara, A., Suda, N., Amari, S., Dualistic differential geometry of positive definite matrices and its applications to related problems, Linear Algebra Appl., Vol. 247 (1996), 31–53.
    • (1996) Linear Algebra Appl , vol.247 , pp. 31-53
    • Ohara, A.1    Suda, N.2    Amari, S.3
  • 11
    • 0030501619 scopus 로고    scopus 로고
    • Monotone metrics on matrix spaces
    • Petz, D., Monotone metrics on matrix spaces, Linear Algebra Appl., Vol. 244 (1996), 81–96.
    • (1996) Linear Algebra Appl , vol.244 , pp. 81-96
    • Petz, D.1
  • 12
    • 85042098591 scopus 로고    scopus 로고
    • Means of positive numbers and matrices
    • Appl., to appear
    • Petz, D., Temesi, R., Means of positive numbers and matrices, SIAM J. Matrix Anal. Appl., to appear.
    • SIAM J. Matrix Anal.
    • Petz, D.1    Temesi, R.2
  • 13
    • 0001438007 scopus 로고
    • Functional calculus for sesquilinear forms and the purification map
    • Pusz, W., Woronowicz, S. L., Functional calculus for sesquilinear forms and the purification map, Rep. Math. Phys., Vol. 8 (1975), 159–170.
    • (1975) Rep. Math. Phys , vol.8 , pp. 159-170
    • Pusz, W.1    Woronowicz, S.L.2
  • 14
    • 0037582222 scopus 로고
    • A Riemannian geometry of the multivariate normal model
    • Skovgaard, L. T., A Riemannian geometry of the multivariate normal model, Scand. J. Statistics, Vol. 11 (1984), 211–223.
    • (1984) Scand. J. Statistics , vol.11 , pp. 211-223
    • Skovgaard, L.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.