University of Oulu

Huhtanen, M., Kotila, V. (2019) Field of optimal quotients and Hermitianity. Linear Algebra and its Applications, 563, 527-547. doi:10.1016/j.laa.2018.11.016

Field of optimal quotients and Hermitianity

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Author: Huhtanen, Marko1; Kotila, Vesa1
Organizations: 1Faculty of Information Technology and Electrical Engineering, University of Oulu
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 3.5 MB)
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Language: English
Published: Elsevier, 2019
Publish Date: 2021-02-15


For an eigenvalue problem, be it generalized or not, the field of optimal quotients is an inclusion region containing the eigenvalues. Convexity properties, connectedness and continuity of this set are addressed. Since any notion of quotients is inherently basis dependent, varying the basis is shown to provide a lot of information. Then, due to its non-convexity, the field of optimal quotients allows recovering the spectrum exactly. In the case of a standard eigenvalue problem, the classical field of values of a matrix is recovered through a limit process. The notion leads to a serious claim how normal, Hermitian and unitary generalized eigenvalue problems should be formulated.

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Series: Linear algebra and its applications
ISSN: 0024-3795
ISSN-E: 0024-3795
ISSN-L: 0024-3795
Volume: 563
Pages: 527 - 547
DOI: 10.1016/j.laa.2018.11.016
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Copyright information: © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license