Nature

Positive Definite Matrices and Their Means

Positive definite matrices play a central role in mathematics, physics, statistics and engineering due to their unique properties and widespread applicability. These matrices, which are characterised ...
JSTOR Daily

GENERALIZED PRECONDITIONED HERMITIAN AND SKEW-HERMITIAN SPLITTING METHODS FOR NON-HERMITIAN POSITIVE-DEFINITE LINEAR SYSTEMS

In this paper, a generalized preconditioned Hermitian and skew-Hermitian splitting (GPHSS) iteration method for a non-Hermitian positive-definite matrix is studied, which covers standard Hermitian and ...
JSTOR Daily

ON HERMITIAN POSITIVE DEFINITE SOLUTIONS OF MATRIX EQUATION X - A*X⁻² A = I

This is a preview. Log in through your library . Abstract The Hermitian positive definite solutions of the matrix equation X — A*X⁻² A = I are studied. A theorem for existence of solutions is given ...
University of Waterloo

Vector Transport Free Riemannian LBFGS for Optimization on Symmetric Positive Definite Matrix Manifolds

We focus on the Symmetric Positive Definite (SPD) manifolds which are beneficial in various fields such as data science and statistics. This work opens a research opportunity for extension of the ...
University of Waterloo

Computational complexity of decomposing a symmetric matrix as a sum of positive semidefinite and diagonal matrices

We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and ...