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Eigenvalue decomposition for tensors of arbitrary rank

Peter Palffy-Muhoray ,Xiaoyu Zheng
Liquid Crystal Institute, Kent State University Dept. of Mathematical Sciences, Kent State University
In many physical situations, the eigenvalues and eigenvectors of tensors are of key importance. Methods for determining eigenvalues and eigenvectors and for implementing eigenvalue decomposition are well known for tensors of second rank. There are many physical situations, however, where knowledge of the eigenvalues and eigenvectors of tensors of higher rank tensors would be useful. We propose a procedure here for determining the eigenvalues and eigenvectors and for implementing eigenvalue decomposition of tensors of arbitrary rank.

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