Existence of real eigenvalues of real tensors. (English) Zbl 1215.15010
The paper deals with the study of the existence of real eigenpairs of real tensors. After giving some basic facts regarding the Brouwer degree of a map, the author uses the Brouwer degree to establish the existence of real eigenpairs of higher-order real tensors in various settings. Some finer criteria for the existence of real eigenpairs of two-dimensional real tensors are also provided. The author gives a complete classification of the Brouwer degree zero and \(\pm 2\) maps induced by general third-order two-dimensionalreal tensors.
Reviewer: Rodica Covaci (Cluj-Napoca)
MSC:
| 15A18 | Eigenvalues, singular values, and eigenvectors |
| 15A69 | Multilinear algebra, tensor calculus |
References:
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