Open AccessSkew compressions of positive definite operators and matrices
Author(s) -
Matteo Polettini,
Albrecht Böttcher
Publication year - 2020
Publication title -
the electronic journal of linear algebra
Language(s) - English
Resource type - Journals
eISSN - 1537-9582
pISSN - 1081-3810
DOI - 10.13001/ela.2020.5335
Subject(s) - mathematics , skew , positive definite matrix , hilbert space , eigenvalues and eigenvectors , singular value , linear operators , pure mathematics , operator (biology) , graph , space (punctuation) , skew symmetric matrix , combinatorics , discrete mathematics , mathematical analysis , symmetric matrix , square matrix , biochemistry , physics , chemistry , repressor , quantum mechanics , astronomy , transcription factor , bounded function , gene , linguistics , philosophy
The paper is devoted to results connecting the eigenvalues and singular values of operators composed by $P^\ast G P$ with those composed in the same way by $QG^{−1}Q^\ast$. Here $P +Q = I$ are skew complementary projections on a finite-dimensional Hilbert space and $G$ is a positive definite linear operator on this space. Also discussed are graph theoretic interpretations of one of the results.