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On the inertia of the block H‐matrices
Author(s) -
Kostić V. R.,
Cvetković Lj.
Publication year - 2017
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2101
Subject(s) - mathematics , block (permutation group theory) , sylvester's law of inertia , block matrix , inertia , matrix (chemical analysis) , diagonal matrix , diagonal , stability (learning theory) , algebra over a field , symmetric matrix , combinatorics , pure mathematics , computer science , eigenvalues and eigenvectors , geometry , physics , materials science , classical mechanics , quantum mechanics , machine learning , composite material
Summary The problem of determining matrix inertia is very important in many applications, for example, in stability analysis of dynamical systems. In the (point‐wise) H‐matrix case, it was proven that the diagonal entries solely reveal this information. This paper generalises these results to the block H‐matrix cases for 1, 2, and ∞ matrix norms. The usefulness of the block approach is illustrated on 3 relevant numerical examples, arising in engineering.