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Continuous decompositions and coalescing eigenvalues for matrices depending on parameters. (English) Zbl 1318.15004
Dieci, Luca (ed.) et al., Current challenges in stability issues for numerical differential equations. Lectures of the CIME-EMS summer school, Cetraro, Italy, June 2011. Cham: Springer; Florence: Fondazione CIME (ISBN 978-3-319-01299-5/pbk; 978-3-319-01300-8/ebook). Lecture Notes in Mathematics 2082. CIME Foundation Subseries, 173-264 (2014).
Summary: This contribution is a summary of four lectures delivered by the first author at the CIME Summer school in June 2011 at Cetraro (Italy). Preparation of those lectures was greatly aided by the other authors of these lecture notes.
Our goal is to present some classical, as well as some new, results related to decompositions of matrices depending on one or more parameters, with particular emphasis being paid to the case of coalescing eigenvalues (or singular values) for matrices depending on two or three parameters. There is an extensive literature on this subject, but a systematic collection of relevant results is lacking, and this provided the impetus for writing the lecture notes.
During the last 15 years, Dieci has had several collaborators on the topics under scrutiny. Besides the coauthors of these lectures, the collaboration with the following people is gratefully acknowledged: Timo Eirola (Helsinki University of Technology, Finland), Jann-Long Chern (National Central University, Taiwan), Mark Friedman (University of Alabama, Huntsville) and Maria Grazia Gasparo (University of Florence, Italy).
For the entire collection see [Zbl 1279.65004].

MSC:
15A18 Eigenvalues, singular values, and eigenvectors
15-02 Research exposition (monographs, survey articles) pertaining to linear algebra
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