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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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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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Ordering positive definite matrices [PDF]
Information Geometry, 2018 We introduce new partial orders on the set Sn+$$S^+_n$$ of positive definite matrices of dimension n derived from the affine-invariant geometry of Sn+$$S^+_n$$. The orders are induced by affine-invariant cone fields, which arise naturally from a local analysis of the orders that are compatible with the homogeneous geometry of Sn+$$S^+_n$$ defined by ...
Cyrus Mostajeran, Rodolphe Sépulchre
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Tensor Sparse Coding for Positive Definite Matrices [PDF]
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2014 In recent years, there has been extensive research on sparse representation of vector-valued signals. In the matrix case, the data points are merely vectorized and treated as vectors thereafter (for example, image patches). However, this approach cannot be used for all matrices, as it may destroy the inherent structure of the data.
Nikos Papanikolopoulos +2 more
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Riemannian Laplace Distribution on the Space of Symmetric Positive Definite Matrices
Entropy, 2016 The Riemannian geometry of the space Pm, of m × m symmetric positive definite matrices, has provided effective ...
Hatem Hajri +4 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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POSITIVE-DEFINITE MATRICES OVER FINITE FIELDS
Rocky Mountain Journal of MathematicsThe study of positive-definite matrices has focused on Hermitian matrices, that is, square matrices with complex (or real) entries that are equal to their own conjugate transposes. In the classical setting, positive-definite matrices enjoy a multitude of equivalent definitions and properties.
Hays Whitlatch
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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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A canonical form for positive definite matrices [PDF]
Open Book Series, 2020 We exhibit an explicit, deterministic algorithm for finding a canonical form for a positive definite matrix under unimodular integral transformations. We use characteristic sets of short vectors and partition-backtracking graph software. The algorithm runs in a number of arithmetic operations that is exponential in the dimension $n$, but it is ...
M. Dutour Sikirić (Mathieu) +3 more
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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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