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.
Original language | English |
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Pages (from-to) | 1581-1595 |
Number of pages | 15 |
Journal | SIAM Journal on Matrix Analysis and Applications |
Volume | 34 |
Issue number | 4 |
DOIs | |
Publication status | Published - 1 Dec 2013 |
Keywords
- Eigenvalue-eigenvector
- Fredholm alternative
- Gelfand formula
- Higher order tensor
- Positively homogeneous
ASJC Scopus subject areas
- Analysis