Results 61 to 70 of about 294,893 (309)

Rank-preserving geometric means of positive semi-definite matrices

, 2012
The generalization of the geometric mean of positive scalars to positive definite matrices has attracted considerable attention since the seminal work of Ando.
Bonnabel, Silvere, Collard, Anne, Sepulchre, Rodolphe   +2 more
core   +1 more source

Minimal zeros of copositive matrices [PDF]

, 2014
Let $A$ be an element of the copositive cone ${\cal C}_n$. A zero $u$ of $A$ is a nonzero nonnegative vector such that $u^TAu = 0$. The support of $u$ is the index set $\mbox{supp}u \subset \{1,\dots,n\}$ corresponding to the positive entries of $u$.
Hildebrand, Roland
core   +6 more sources

Products of positive semi-definite matrices

Linear Algebra and its Applications, 2017
It is known that every complex square matrix with nonnegative determinant is the product of positive semi-definite matrices. There are characterizations of matrices that require two or five positive semi-definite matrices in the product. However, the characterizations of matrices that require three or four positive semi-definite matrices in the product
Cui, Jianlian, Li, Chi-Kwong, Sze, Nung-Sing   +2 more
openaire   +2 more sources

Procrustes problems in Riemannian manifolds of positive definite matrices

Linear Algebra and its Applications, 2019
We consider the manifold of positive definite matrices endowed with the Fisher Riemannian metric and some other distances commonly used in information theory.
R. Bhatia, M. Congedo
semanticscholar   +1 more source

Dimensionality reduction based on distance preservation to local mean for symmetric positive definite matrices and its application in brain–computer interfaces [PDF]

Journal of Neural Engineering, 2016
Objective. In this paper, we propose a nonlinear dimensionality reduction algorithm for the manifold of symmetric positive definite (SPD) matrices that considers the geometry of SPD matrices and provides a low-dimensional representation of the manifold ...
Alireza Davoudi, S. S. Ghidary, Khadijeh Sadatnejad   +2 more
semanticscholar   +1 more source

A Non-Iterative Method for the Difference of Means on the Lie Group of Symmetric Positive-Definite Matrices

Mathematics, 2022
A non-iterative method for the difference of means is presented to calculate the log-Euclidean distance between a symmetric positive-definite matrix and the mean matrix on the Lie group of symmetric positive-definite matrices.
Xiaomin Duan, Xueting Ji, Huafei Sun, Hao Guo   +3 more
doaj   +1 more source

On directional derivatives of trace functionals of the form $A\mapsto\Tr(Pf(A))$

, 2018
Given a function $f:(0,\infty)\rightarrow\RR$ and a positive semidefinite $n\times n$ matrix $P$, one may define a trace functional on positive definite $n\times n$ matrices as $A\mapsto \Tr(Pf(A))$.
Girard, Mark W.
core   +1 more source

Dictionary Learning of Symmetric Positive Definite Data Based on Riemannian Manifold Tangent Spaces and Local Homeomorphism

IEEE Access, 2022
Symmetric Positive Definite (SPD) data are increasingly prevalent in dictionary learning recently. SPD data are the typical non-Euclidean data and cannot constitute a Euclidean space.
Hui He, Shuyu Liu, Zhengming Ma, Weijia Feng   +3 more
doaj   +1 more source

Riemannian Gaussian Distributions on the Space of Symmetric Positive Definite Matrices [PDF]

IEEE Transactions on Information Theory, 2015
Data, which lie in the space $\mathcal {P}_{m\,}$ , of $m \times m$ symmetric positive definite matrices, (sometimes called tensor data), play a fundamental role in applications, including medical imaging, computer vision, and radar signal processing.
S. Said, L. Bombrun, Y. Berthoumieu, J. Manton   +3 more
semanticscholar   +1 more source

An Adaptive Human Pilot Model With Reaction Time Delay for Enhanced Adaptive Control in Piloted Systems

International Journal of Adaptive Control and Signal Processing, EarlyView.
This work introduces an adaptive human pilot model that captures pilot time‐delay effects in adaptive control systems. The model enables the prediction of pilot–controller interactions, facilitating safer integration and improved design of adaptive controllers for piloted applications.
Abdullah Habboush, Yildiray Yildiz
wiley   +1 more source