Linear Expand-Contract Plasticity of Ellipsoids Revisited

TL;DR

This paper revisits the concept of linear expand-contract plasticity of ellipsoids, providing a spectral description of these geometric objects in terms of bounded self-adjoint operators.

Contribution

It offers a spectral characterization of linear expand-contract plastic ellipsoids, enhancing understanding of their structure via quadratic forms and operator spectra.

Findings

Spectral description of plastic ellipsoids

Connection between quadratic forms and ellipsoid plasticity

Enhanced understanding of ellipsoid geometry in operator theory

Abstract

This work is aimed to describe linear expand-contract plastic ellipsoids given via quadratic form of a bounded positively defined self-adjoint operator in terms of its spectrum.