-
1
-
-
79958810366
-
Operator log-convex functions and operator means
-
Ando T., Hiai F. Operator log-convex functions and operator means. Math. Ann. 2011, 350:611-630.
-
(2011)
Math. Ann.
, vol.350
, pp. 611-630
-
-
Ando, T.1
Hiai, F.2
-
3
-
-
34548412123
-
Geometric means in a novel vector space structure on symmetric positive-definite matrices
-
Arsigny V., Fillard P., Pennec X., Ayache N. Geometric means in a novel vector space structure on symmetric positive-definite matrices. SIAM J. Matrix Anal. Appl. 2006, 29:328-347.
-
(2006)
SIAM J. Matrix Anal. Appl.
, vol.29
, pp. 328-347
-
-
Arsigny, V.1
Fillard, P.2
Pennec, X.3
Ayache, N.4
-
4
-
-
84855222035
-
-
Riemannian geometry applied to BCI classification, preprint.
-
A. Barachant, S. Bonnet, M. Congedo, C. Jutten, Riemannian geometry applied to BCI classification, preprint.
-
-
-
Barachant, A.1
Bonnet, S.2
Congedo, M.3
Jutten, C.4
-
5
-
-
67649985691
-
Interactions between symmetric cone and information geometries: Bruhat-Tits and Siegel spaces models for higher resolution autoregressive doppler imagery
-
Barbaresco F. Interactions between symmetric cone and information geometries: Bruhat-Tits and Siegel spaces models for higher resolution autoregressive doppler imagery. Lecture Notes in Comput. Sci. 2009, vol. 5416:124-163.
-
(2009)
Lecture Notes in Comput. Sci.
, vol.5416
, pp. 124-163
-
-
Barbaresco, F.1
-
7
-
-
79958793902
-
Completely positive mappings and mean matrices
-
Besenyei A., Petz D. Completely positive mappings and mean matrices. Linear Algebra Appl. 2011, 435:984-997.
-
(2011)
Linear Algebra Appl.
, vol.435
, pp. 984-997
-
-
Besenyei, A.1
Petz, D.2
-
8
-
-
0004151496
-
-
Springer-Verlag, New York
-
Bhatia R. Matrix Analysis 1997, Springer-Verlag, New York.
-
(1997)
Matrix Analysis
-
-
Bhatia, R.1
-
9
-
-
0142094477
-
On the exponential metric increasing property
-
Bhatia R. On the exponential metric increasing property. Linear Algebra Appl. 2003, 375:211-220.
-
(2003)
Linear Algebra Appl.
, vol.375
, pp. 211-220
-
-
Bhatia, R.1
-
10
-
-
84883937488
-
Positive Definite Matrices
-
Princeton University Press, Princeton, NJ
-
Bhatia R. Positive Definite Matrices. Princeton Ser. Appl. Math. 2007, Princeton University Press, Princeton, NJ.
-
(2007)
Princeton Ser. Appl. Math.
-
-
Bhatia, R.1
-
11
-
-
31444440896
-
Riemannian geometry and matrix geometric means
-
Bhatia R., Holbrook J. Riemannian geometry and matrix geometric means. Linear Algebra Appl. 2006, 413:594-618.
-
(2006)
Linear Algebra Appl.
, vol.413
, pp. 594-618
-
-
Bhatia, R.1
Holbrook, J.2
-
12
-
-
84863307042
-
Monotonicity of the matrix geometric mean
-
in press. doi:10.1007/s00208-011-0721-9
-
R. Bhatia, R. Karandikar, Monotonicity of the matrix geometric mean, Math. Ann., in press. doi:10.1007/s00208-011-0721-9.
-
Math. Ann.
-
-
Bhatia, R.1
Karandikar, R.2
-
13
-
-
34247887617
-
Mean matrices and infinite divisibility
-
Bhatia R., Kosaki H. Mean matrices and infinite divisibility. Linear Algebra Appl. 2007, 424:36-54.
-
(2007)
Linear Algebra Appl.
, vol.424
, pp. 36-54
-
-
Bhatia, R.1
Kosaki, H.2
-
14
-
-
84855222036
-
-
Computing the Karcher mean of symmetric positive definite matrices, preprint.
-
D. Bini, B. Iannazzo, Computing the Karcher mean of symmetric positive definite matrices, preprint.
-
-
-
Bini, D.1
Iannazzo, B.2
-
15
-
-
77952792929
-
An effective matrix geometric mean satisfying the Ando-Li-Mathias properties
-
Bini D., Meini B., Poloni F. An effective matrix geometric mean satisfying the Ando-Li-Mathias properties. Math. Comp. 2010, 79:437-452.
-
(2010)
Math. Comp.
, vol.79
, pp. 437-452
-
-
Bini, D.1
Meini, B.2
Poloni, F.3
-
16
-
-
84972570848
-
Convexity of the geodesic distance on spaces of positive operators
-
Corach G., Porta H., Recht L. Convexity of the geodesic distance on spaces of positive operators. Illinois J. Math. 1994, 38:87-94.
-
(1994)
Illinois J. Math.
, vol.38
, pp. 87-94
-
-
Corach, G.1
Porta, H.2
Recht, L.3
-
18
-
-
84980162923
-
Riemannian center of mass and mollifier smoothing
-
Karcher H. Riemannian center of mass and mollifier smoothing. Comm. Pure Appl. Math. 1977, 30:509-541.
-
(1977)
Comm. Pure Appl. Math.
, vol.30
, pp. 509-541
-
-
Karcher, H.1
-
19
-
-
0000472839
-
Means of positive linear operators
-
Kubo F., Ando T. Means of positive linear operators. Math. Ann. 1980, 246:205-224.
-
(1980)
Math. Ann.
, vol.246
, pp. 205-224
-
-
Kubo, F.1
Ando, T.2
-
20
-
-
0004089466
-
Fundamentals of Differential Geometry
-
Springer
-
Lang S. Fundamentals of Differential Geometry. Grad. Texts in Math. 1999, Springer.
-
(1999)
Grad. Texts in Math.
-
-
Lang, S.1
-
21
-
-
34848813795
-
Symmetric spaces with convex metrics
-
Lawson J., Lim Y. Symmetric spaces with convex metrics. Forum Math. 2007, 19:571-602.
-
(2007)
Forum Math.
, vol.19
, pp. 571-602
-
-
Lawson, J.1
Lim, Y.2
-
22
-
-
39749192606
-
Metric convexity of symmetric cones
-
Lawson J., Lim Y. Metric convexity of symmetric cones. Osaka J. Math. 2007, 44:795-816.
-
(2007)
Osaka J. Math.
, vol.44
, pp. 795-816
-
-
Lawson, J.1
Lim, Y.2
-
23
-
-
77955948060
-
A general framework for extending means to higher orders
-
Lawson J., Lim Y. A general framework for extending means to higher orders. Colloq. Math. 2008, 113:191-221.
-
(2008)
Colloq. Math.
, vol.113
, pp. 191-221
-
-
Lawson, J.1
Lim, Y.2
-
24
-
-
80052714557
-
Monotonic properties of the least squares mean
-
Lawson J., Lim Y. Monotonic properties of the least squares mean. Math. Ann. 2011, 351:267-279.
-
(2011)
Math. Ann.
, vol.351
, pp. 267-279
-
-
Lawson, J.1
Lim, Y.2
-
25
-
-
79952748045
-
Multi-variable weighted geometric means of positive definite matrices
-
Lee H., Lim Y., Yamazaki T. Multi-variable weighted geometric means of positive definite matrices. Linear Algebra Appl. 2011, 435:307-322.
-
(2011)
Linear Algebra Appl.
, vol.435
, pp. 307-322
-
-
Lee, H.1
Lim, Y.2
Yamazaki, T.3
-
26
-
-
39749152784
-
On Ando-Li-Mathias geometric mean equations
-
Lim Y. On Ando-Li-Mathias geometric mean equations. Linear Algebra Appl. 2008, 428:1767-1777.
-
(2008)
Linear Algebra Appl.
, vol.428
, pp. 1767-1777
-
-
Lim, Y.1
-
27
-
-
84861099313
-
Some inequalities for unitarily invariant norms
-
in press. doi:10.1016/j.laa.2010.08.013
-
J. Matharu, J. Aujla, Some inequalities for unitarily invariant norms, Linear Algebra Appl., in press. doi:10.1016/j.laa.2010.08.013.
-
Linear Algebra Appl.
-
-
Matharu, J.1
Aujla, J.2
-
28
-
-
22944439423
-
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. 2005, 26:735-747.
-
(2005)
SIAM J. Matrix Anal. Appl.
, vol.26
, pp. 735-747
-
-
Moakher, M.1
-
29
-
-
33645812768
-
On the averaging of symmetric positive-definite tensors
-
Moakher M. On the averaging of symmetric positive-definite tensors. J. Elasticity 2006, 82:273-296.
-
(2006)
J. Elasticity
, vol.82
, pp. 273-296
-
-
Moakher, M.1
-
30
-
-
0042410954
-
Compressions of infinite-dimensional bounded symmetric domains
-
Neeb K.-H. Compressions of infinite-dimensional bounded symmetric domains. Semigroup Forum 2001, 61:71-105.
-
(2001)
Semigroup Forum
, vol.61
, pp. 71-105
-
-
Neeb, K.-H.1
-
31
-
-
84855222175
-
-
Classification of affine matrix means, preprint, 2011.
-
M. Pálfia, Classification of affine matrix means, preprint, 2011.
-
-
-
Pálfia, M.1
-
32
-
-
84966219504
-
On certain contraction mappings in a partially ordered vector space
-
Thompson A.C. On certain contraction mappings in a partially ordered vector space. Proc. Amer. Math. Soc. 1963, 14:438-443.
-
(1963)
Proc. Amer. Math. Soc.
, vol.14
, pp. 438-443
-
-
Thompson, A.C.1
-
33
-
-
84855212071
-
-
The Riemannian mean and matrix inequalities related to the Ando-Hiai inequality and Chaotic order, Oper. Matrices, in press.
-
T. Yamazaki, The Riemannian mean and matrix inequalities related to the Ando-Hiai inequality and Chaotic order, Oper. Matrices, in press.
-
-
-
Yamazaki, T.1
|