Orthogonal Tensor Decompositions
- 1 January 2001
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Matrix Analysis and Applications
- Vol. 23 (1), 243-255
- https://doi.org/10.1137/s0895479800368354
Abstract
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].Keywords
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