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References
21
[1]
[A] T. Ando,Topics on Operator Inequalities, Lecture Notes, Hokkaido University, Sapporo, 1978.
[2]
[ALM] T. Ando, C.-K. Li, and R. Mathias, Geometric means,Linear Algebra Appl. 385(2004), 305–334. 10.1016/j.laa.2003.11.019
[3]
[Be] M. Berger,A Panoramic View of Riemannian Geometry, Springer-Verlag, 2003. 10.1007/978-3-642-18245-7
[4]
[B] R. Bhatia,Matrix Analysis, Springer-Verlag, 1997. 10.1007/978-1-4612-0653-8
[5]
[B2] R. Bhatia, On the exponential metric increasing property,Linear Algebra Appl. 375(2003), 211–220. 10.1016/s0024-3795(03)00647-5
[6]
[BH] R. Bhatia and J. Holbrook, Riemannian geometry and matrix geometric means, to appear inLinear Algebra Appl.
[7]
[BrHa] M. Bridson and A. Haefliger,Metric Spaces of Nonpositive Curvature, Springer-Verlag, 1999. 10.1007/978-3-662-12494-9
[8]
[BMV] P. S. Bullen, D. S. Mitrinovic, and P. M. Vasic,Means and Their Inequalities, D. Reidel, Dordrecht, 1988. 10.1007/978-94-017-2226-1
[9]
[BS] K. V. Bhagwat and R. Subramanian, Inequalities between means of positive operators,Math. Proc. Camb. Phil. Soc. 83(1978), 393-401. 10.1017/s0305004100054670
[10]
[CPR] G. Corach, H. Porta, and L. Recht, Geodesics and operator means in the space of positive operators,Int. J. Math. 4(1993), 193–202. 10.1142/s0129167x9300011x
[11]
[FLS] R. Feynman, R. Leighton, and M. Sands,The Feynman Lectures on Physics, volume 3, page 20–17, Addison-Wesley, 1965. 10.1063/1.3051743
[12]
[HLP] G. H. Hardy, J. E. Littlewood, and G. Pólya,Inequalities, Cambridge University Press, 1934.
[13]
[K] B. Kostant, On convexity, the Weyl group and the Iwasawa decomposition,Ann. Sc. E. N. S. 6(1973), 413–455.
[14]
[KA] F. Kubo and T. Ando, Means of positive linear operators,Math. Ann. 246(1980), 205–224. 10.1007/bf01371042
[15]
[LL] J. D. Lawson and Y. Lim, The geometric mean, matrices, metrics, and more,Amer. Math. Monthly 108(2001), 797–812. 10.2307/2695553
[16]
[M] M. Moakher, A differential geometric approach to the geometric mean of symmetric positive-definite matrices,SIAM J. Matrix Anal. Appl. 26(2005), 735–747. 10.1137/s0895479803436937
[17]
[P] B. Pascal,Pensees, translation by W. F. Trotter, excerpt from item 72, Encyclopaedia Britannica, Great Books 33, 1952.
[18]
[Po] H. Poincare,Science and Hypothesis, from page 50 of the Dover reprint, Dover Publications, 1952.
[19]
[PW] W. Pusz and S. L. Woronowicz, Functional calculus for sesquilinear forms and the purification map,Reports Math. Phys. 8(1975), 159–170. 10.1016/0034-4877(75)90061-0
[20]
[S] I. Segal, Notes towards the construction of nonlinear relativistic quantum fields III,Bull. Amer. Math. Soc. 75(1969), 1390–1395. 10.1090/s0002-9904-1969-12429-8
[21]
[Si] B. Simon,Trace Ideals and Their Applications, Cambridge University Press, 1979.
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Bulletin des Sciences Mathématiques
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Published
Dec 01, 2006
Vol/Issue
28(1)
Pages
32-39
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Cite This Article
John Holbrook, Rajendra Bhatia (2006). Noncommutative geometric means. The Mathematical Intelligencer, 28(1), 32-39. https://doi.org/10.1007/bf02987000
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