Open AccessExact conditions for preservation of the partial indices of a perturbed triangular 2 × 2 matrix function
Author(s) -
В. М. Адуков,
Gennady Mishuris,
Sergei Rogosin
Publication year - 2020
Publication title -
proceedings of the royal society a mathematical physical and engineering sciences
Language(s) - English
Resource type - Journals
eISSN - 1471-2946
pISSN - 1364-5021
DOI - 10.1098/rspa.2020.0099
Subject(s) - mathematics , matrix function , matrix (chemical analysis) , partial derivative , factorization , perturbation (astronomy) , unit circle , triangular matrix , class (philosophy) , matrix decomposition , parametric statistics , set (abstract data type) , partial differential equation , mathematical analysis , pure mathematics , symmetric matrix , computer science , algorithm , physics , statistics , eigenvalues and eigenvectors , materials science , quantum mechanics , invertible matrix , artificial intelligence , composite material , programming language
The possible instability of partial indices is one of the important constraints in the creation of approximate methods for the factorization of matrix functions. This paper is devoted to a study of a specific class of triangular matrix functions given on the unit circle with a stable and unstable set of partial indices. Exact conditions are derived that guarantee a preservation of the unstable set of partial indices during a perturbation of a matrix within the class. Thus, even in this probably simplest of cases, when the factorization technique is well developed, the structure of the parametric space (guiding the types of matrix perturbations) is non-trivial.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom