Year: 2016
Type: preprint
Abstract: A non-degenerate two-dimensional linear operator $φ$ transforms the unit circle into ellipse. Let $p$ be the length of its bigger axis and $q$ -- the length of smaller. We can define the deformation coefficient $k(φ)$ as $q/p$. Analogously, if $φ$ is a non-degenerate three-dimensional operator, then it transforms the unit sphere into ellipsoid. If $p>q>r$ are lengths of its axes, then deformation coefficient $k(φ)$ will be defined as $r/p$. In this work we compute the mean value of deformation coefficient in two-dimensional case and give an estimation of mean value in three-dimensional case.
Source: arXiv (Cornell University)
Authors: Busjatskaja, Irina, Kochetkov, Yury
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2502308963