Exact conditions for preservation of the partial indices of a perturbed triangular 2 × 2 matrix function

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Type Article
Original languageEnglish
Article number20200099
Number of pages19
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2237
Publication statusPublished - 27 May 2020
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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.


  • Essential polynomials, Factorization of matrix functions, Toeplitz matrix, Triangular matrices, Wiener algebra