Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/9231
Title: Spectral properties of positively homogeneous operators induced by higher order tensors.
Authors: Song, Y
Qi, L 
Keywords: Eigenvalue-eigenvector
Fredholm alternative
Gelfand formula
Higher order tensor
Positively homogeneous
Issue Date: 2013
Publisher: Society for Industrial and Applied Mathematics
Source: SIAM journal on matrix analysis and applications, 2013, v. 34, no. 4, p. 1581-1595 How to cite?
Journal: SIAM journal on matrix analysis and applications 
Abstract: The Fredholm alternative type results are proved for eigenvalues (E-eigenvalues, H-eigenvalues, Z-eigenvalues) of a higher order tensor A. For the positively homogeneous operators FA and TA induced by a higher order tensor A, we show some relationship between the Gelfand formula and the spectral radius, and present the upper bound of their spectral radii. Furthermore, for a nonnegative tensor A, we obtain the practical relevance for the spectral radius of the operators FA and TA as well as the operator norms of FA and TA.
URI: http://hdl.handle.net/10397/9231
ISSN: 0895-4798
EISSN: 1095-7162
DOI: 10.1137/130909135
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