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On eigenvalues of rectangular matrices
Stockholm University, Faculty of Science, Department of Mathematics.
Dept of Maths, Michigan State University.
2009 (English)In: Proceedings of the Steklov Institute of Mathematics, ISSN 0081-5438, E-ISSN 1531-8605, Vol. 267, no 1, 248-255 p.Article in journal (Refereed) Published
Abstract [en]

 Given a (k+1)-tuple A,B (1), ..., B (k) of mxn matrices with m a parts per thousand currency sign n, we call the set of all k-tuples of complex numbers {lambda (1), ..., lambda k} such that the linear combination A+lambda (1) B (1)+lambda (2) B (2)+ ... +lambda (k) B (k) has rank smaller than m the eigenvalue locus of the latter pencil. Motivated primarily by applications to multiparameter generalizations of the Heine-Stieltjes spectral problem, we study a number of properties of the eigenvalue locus in the most important case k = n-m+1.

Place, publisher, year, edition, pages
2009. Vol. 267, no 1, 248-255 p.
Keyword [en]
eigenvalues, rectangular matrices
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-49753DOI: 10.1134/S0081543809040208ISI: 000274252700020OAI: oai:DiVA.org:su-49753DiVA: diva2:379361
Available from: 2010-12-31 Created: 2010-12-17 Last updated: 2017-12-11Bibliographically approved

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