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Linear algebra and its applications, ISSN 0024-3795, 2004, Volume 385, Issue 1-3, pp. 305 - 334
We propose a definition for geometric mean of k positive (semi) definite matrices. We show that our definition is the only one in the literature that has the... 
Positive semidefinite matrix | Matrix inequality | Geometric mean | Matrix square root | Spectral radius | matrix square root | MATHEMATICS, APPLIED | positive semidefinite matrix | spectral radius | geometric mean | matrix inequality
Journal Article
Journal Article
Biomechanics and modeling in mechanobiology, ISSN 1617-7940, 2017, Volume 17, Issue 2, pp. 351 - 366
Journal Article
The Annals of statistics, ISSN 0090-5364, 2010, Volume 38, Issue 2, pp. 1034 - 1070
Journal Article
Journal of Complex Networks, ISSN 2051-1310, 2018, Volume 6, Issue 2, pp. 157 - 172
.... This formulation provides a geometric interpretation of Markov Stability in terms of a time-dependent spectral embedding, where the Markov time acts as an inhomogeneous geometric resolution factor... 
Partitioning algorithms | Markov stability | Multiscale community detection | Modularity | Spectral methods
Journal Article
The Visual Computer, ISSN 0178-2789, 5/2009, Volume 25, Issue 5, pp. 667 - 675
.... Our method extracts salient geometric feature points in the Laplace–Beltrami spectral domain instead of usual spatial domains... 
Computer Graphics | Spectral geometry | Computer Science | Image Processing and Computer Vision | Shape matching | Artificial Intelligence (incl. Robotics) | Geometric analysis | COMPUTER SCIENCE, SOFTWARE ENGINEERING
Journal Article
ACM Transactions on Graphics (TOG), ISSN 0730-0301, 07/2019, Volume 38, Issue 4, pp. 1 - 13
We introduce a novel approach to measure the behavior of a geometric operator before and after... 
geometry processing | numerical coarsening | spectral geometry | COMPUTER SCIENCE, SOFTWARE ENGINEERING | SPARSE
Journal Article
Linear and Multilinear Algebra, ISSN 0308-1087, 08/2019, Volume 67, Issue 8, pp. 1637 - 1652
... on sequence spaces, or of the Hadamard geometric mean and ordinary products of positive kernel operators on Banach function spaces... 
nonnegative matrices | Secondary: 47A10 | positive kernel operators | Hadamard-Schur weighted geometric mean | Banach function spaces | spectral radius | Primary: 47B65 | MATHEMATICS | PRODUCTS | BOUNDED SETS | JOINT | Kernels | Operators (mathematics) | Function space | Inequalities
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 10/2017, Volume 531, pp. 268 - 280
.... We show that the weighted means satisfying the arithmetic-geometric-harmonic mean inequalities are the multivariate Lie-Trotter means... 
Arithmetic-geometric-harmonic mean inequalities | Lie-Trotter formula | Inductive mean | Geometric mean | Spectral geometric mean | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 11/2012, Volume 437, Issue 9, pp. 2159 - 2172
In this paper we provide a new class of (metric) geometric means of positive definite matrices varying over Hermitian unitary matrices... 
Hermitian unitary matrix | Hadamard space | Geometric mean | Factorization | Spectral geometric mean | Positive definite matrix | MATHEMATICS | MATHEMATICS, APPLIED | SUBMANIFOLDS | ANDO-LI-MATHIAS
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 2007, Volume 427, Issue 2, pp. 190 - 196
Journal Article
Proceedings of the National Academy of Sciences - PNAS, ISSN 1091-6490, 2005, Volume 102, Issue 21, pp. 7426 - 7431
Journal Article
Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, 06/2014, Volume 57, Issue 2, pp. 565 - 571
...–Heinz inequality means that A ≤ B implies that Aa ≦ Ba. We show that A ≤ B if and only if (A + λ)a ≦ (B + λ)a for every λ > 0. We then apply this to the geometric mean and spectral order. 
Loewner-Heinz inequality | geometric mean | spectral order | MATHEMATICS | Geometry | Applied mathematics | Algebra | Operators | Spectra | Real numbers | Mathematical analysis | Inequalities
Journal Article