Approximate joint diagonalization and geometric mean of symmetric positive definite matrices. [PDF]
PLoS ONE, 2014 We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD) matrices and their approximate joint ...
Marco Congedo +3 more
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On The Frobenius Condition Number of Positive Definite Matrices [PDF]
Journal of Inequalities and Applications, 2010 We present some lower bounds for the Frobenius condition number of a positive definite matrix depending on trace, determinant, and Frobenius norm of a positive definite matrix and compare these results with other results.
Türkmen Ramazan +1 more
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Rotation-based metric on the Riemannian manifold of SPD matrices with applications to source data selection for brain-computer interface transfer learning [PDF]
Frontiers in Human NeuroscienceThis paper introduces the pole ratio metric and presents a sphere-based view of symmetric positive-definite matrix rotations on the Riemannian manifold of symmetric positive-definite matrices equipped with the affine-invariant Riemannian metric. The pole
Frida Heskebeck +2 more
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Intrinsic Regression Models for Positive-Definite Matrices With Applications to Diffusion Tensor Imaging [PDF]
Journal of the American Statistical Association, 2009 Weili Lin, Hongtu Zhu
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mbend: an R package for bending non-positive-definite symmetric matrices to positive-definite
BMC Genetics, 2020 Background R package mbend was developed for bending symmetric non-positive-definite matrices to positive-definite (PD). Bending is a procedure of transforming non-PD matrices to PD.
Mohammad Ali Nilforooshan
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Convex maps on $\protect \mathbb{R}^n$ and positive definite matrices
Comptes Rendus. Mathématique, 2020 We obtain several convexity statements involving positive definite matrices. In particular, if $A,B,X,Y$ are invertible matrices and $A,B$ are positive, we show that the map \[ (s,t) \mapsto \mathrm{Tr}\,\log \left(X^*A^sX + Y^*B^tY\right) \] is jointly ...
Bourin, Jean-Christophe, Shao, Jingjing
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Gyrovector Spaces on the Open Convex Cone of Positive Definite Matrices [PDF]
Mathematics Interdisciplinary Research, 2016 In this article we review an algebraic definition of the gyrogroup and a simplified version of the gyrovector space with two fundamental examples on the open ball of finite-dimensional Euclidean spaces, which are the Einstein and Möbius gyrovector ...
Sejong Kim
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Positive Definite Norm Dependent Matrices In Stochastic Modeling
Demonstratio Mathematica, 2014 Positive definite norm dependent matrices are of interest in stochastic modeling of distance/norm dependent phenomena in nature. An example is the application of geostatistics in geographic information systems or mathematical analysis of varied spatial ...
Kuniewski Sebastian P. +1 more
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A New Slack Lyapunov Functional for Dynamical System with Time Delay
Mathematics, 2022 The traditional method of constructing a Lyapunov functional for dynamical systems with time delay is usually dependent on positive definite matrices in the quadratic form.
Can Zhao +3 more
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Geometrical Inverse Preconditioning for Symmetric Positive Definite Matrices
Mathematics, 2016 We focus on inverse preconditioners based on minimizing F ( X ) = 1 − cos ( X A , I ) , where X A is the preconditioned matrix and A is symmetric and positive definite. We present and analyze gradient-type methods to minimize F ( X )
Jean-Paul Chehab, Marcos Raydan
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