Intrinsic Regression Models for Positive-Definite Matrices With Applications to Diffusion Tensor Imaging. [PDF]
J Am Stat Assoc, 2009 Zhu H +5 more
europepmc +2 more sources
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
doaj +1 more source
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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Metrics induced by Jensen-Shannon and related divergences on positive definite matrices [PDF]
Linear Algebra and its Applications, 2019 We study metric properties of symmetric divergences on Hermitian positive definite matrices. In particular, we prove that the square root of these divergences is a distance metric.
S. Sra
semanticscholar +1 more source
On The Frobenius Condition Number of Positive Definite Matrices
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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Products of positive definite matrices. II [PDF]
Pacific Journal of Mathematics, 1967 I. The author gives, for every positive integer \(j\), necessary and sufficient conditions for a \(2\times 2\) real matrix (with positive determinant) to be a product of \(j\) positive definite real symmetric matrices (if \(j\ge 5\), every real matrix with positive determinant can be written as such a product).
openaire +6 more sources
Interacting diffusions on positive definite matrices [PDF]
Probability theory and related fields, 2019 We consider systems of Brownian particles in the space of positive definite matrices, which evolve independently apart from some simple interactions. We give examples of such processes which have an integrable structure.
N. O’Connell
semanticscholar +1 more source
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 Definiteness and Semi-Definiteness of Even Order Symmetric Cauchy Tensors [PDF]
, 2014 Motivated by symmetric Cauchy matrices, we define symmetric Cauchy tensors and their generating vectors in this paper. Hilbert tensors are symmetric Cauchy tensors.
Chen, Haibin, Qi, Liqun
core +1 more source
Hermitian positive definite Toeplitz matrices and Hessenberg matrices [PDF]
Computational and Mathematical Methods, 2019 In the context of orthogonal polynomials, an interesting class of Hermitian positive definite (HPD) matrices are those that are moment matrices with respect to a measure μ with support on the complex plane. In a more general framework, we establish a one-to-one correspondence between infinite upper Hessenberg matrices with positive subdiagonal and HPD ...
Escribano Iglesias, M. del Carmen +2 more
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