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    On the largest eigenvalue of a symmetric nonnegative tensor

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    Fulltext not available
    Authors
    Zhou, Guanglu
    Qi, L.
    Wu, S.
    Date
    2013
    Type
    Journal Article
    
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    Citation
    Zhou, Guanglu and Qi, Liqun and Wu, Soon-Yi. 2013. On the largest eigenvalue of a symmetric nonnegative tensor. Numerical Linear Algebra with Applications. 20 (6): pp. 913-918.
    Source Title
    Numerical Linear Algebra with Applications
    DOI
    10.1002/nla.1885
    ISSN
    1099-1506
    URI
    http://hdl.handle.net/20.500.11937/25034
    Collection
    • Curtin Research Publications
    Abstract

    In this paper, some important spectral characterizations of symmetric nonnegative tensors are analyzed. In particular, it is shown that a symmetric nonnegative tensor has the following properties: (i) its spectral radius is zero if and only if it is a zero tensor; (ii) it is weakly irreducible (respectively, irreducible) if and only if it has a unique positive (respectively, nonnegative) eigenvalue–eigenvector; (iii) the minimax theorem is satisfied without requiring the weak irreducibility condition; and (iv) if it is weakly reducible, then it can be decomposed into some weakly irreducible tensors. In addition, the problem of finding the largest eigenvalue of a symmetric nonnegative tensor is shown to be equivalent to finding the global solution of a convex optimization problem. Subsequently, algorithmic aspects for computing the largest eigenvalue of symmetric nonnegative tensors are discussed.

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