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Spectral test of reducibility for matrix tuples.

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Title: Spectral test of reducibility for matrix tuples.
Authors: Stessin, Michael1 (AUTHOR) mstessin@albany.edu, Yang, Rongwei1 (AUTHOR) ryang@albany.edu
Source: Linear Algebra & its Applications. Oct2026, Vol. 747, p254-273. 20p.
Subjects: Invariant subspaces, Matrices (Mathematics), Algebraic varieties
Abstract: The existence of a common invariant subspace for a matrix tuple implies that its projective joint spectrum possesses an algebraic component. The converse, however, does not hold in general–algebraic components can appear without an associated invariant subspace. In this paper, we address this issue from a multivariable viewpoint and provide necessary and sufficient conditions for when such a correspondence occurs. [ABSTRACT FROM AUTHOR]
Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 195184004
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Spectral test of reducibility for matrix tuples.
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  Data: The existence of a common invariant subspace for a matrix tuple implies that its projective joint spectrum possesses an algebraic component. The converse, however, does not hold in general–algebraic components can appear without an associated invariant subspace. In this paper, we address this issue from a multivariable viewpoint and provide necessary and sufficient conditions for when such a correspondence occurs. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.laa.2026.06.008
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      – Code: eng
        Text: English
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        PageCount: 20
        StartPage: 254
    Subjects:
      – SubjectFull: Invariant subspaces
        Type: general
      – SubjectFull: Matrices (Mathematics)
        Type: general
      – SubjectFull: Algebraic varieties
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      – TitleFull: Spectral test of reducibility for matrix tuples.
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            NameFull: Stessin, Michael
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              Text: Oct2026
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              Y: 2026
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