Journal
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
Volume 23, Issue 1, Pages 243-255Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S0895479800368354
Keywords
tensor decomposition; singular value decomposition; principal components analysis; multidimensional arrays
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We explore the orthogonal decomposition of tensors ( also known as multidimensional arrays or n-way arrays) using two different definitions of orthogonality. We present numerous examples to illustrate the difficulties in understanding such decompositions. We conclude with a counterexample to a tensor extension of the Eckart-Young SVD approximation theorem by Leibovici and Sabatier [Linear Algebra Appl., 269 (1998), pp. 307-329].
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