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 ...

This book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real numbers ...

A new class of large-sample covariance and spectral density matrix estimators is proposed based on the notion of flat-top kernels. The new estimators are shown to be higher-order accurate when ...

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 ...

Left: Illustration of different geometric mean properties on the manifold of positive semidefinite matrices implemented in this library. Deviation of the geometric means computed using the ...

Abstract: Log-Euclidean distances are commonly used to quantify the similarity between positive definite matrices using geometric considerations. This paper analyzes the behavior of this distance when ...

This repository illustrates how matrix control barrier functions (MCBFs) can be used to handle semidefinite matrix constraints, using a connectivity maintenance problem in multi-agent systems as a ...