# A Counterexample to the Possibility of an Extension of the Eckart-Young Low-rank Approximation Theorem for the Orthogonal Rank Tensor Decomposition

### Abstract

Earlier work has shown that no extension of the Eckart–Young SVD approximation theorem can be made to the strong orthogonal rank tensor decomposition. Here, we present a counterexample to the extension of the Eckart–Young SVD approximation theorem to the orthogonal rank tensor decomposition, answering an open question previously posed by Kolda [SIAM J. Matrix Anal. Appl., 23 (2001), pp. 243–355].

Type
Publication
SIAM Journal on Matrix Analysis and Applications
Date
Tags
Citation
T. G. Kolda. A Counterexample to the Possibility of an Extension of the Eckart-Young Low-rank Approximation Theorem for the Orthogonal Rank Tensor Decomposition. SIAM Journal on Matrix Analysis and Applications, Vol. 24, No. 3, pp. 762-767, 2003. https://doi.org/10.1137/S0895479801394465

### Keywords

singular value decomposition, principal components analysis, multidimensional arrays, higher-order tensor, multilinear algebra

### BibTeX

@article{Ko03,
author = {Tamara G. Kolda},
title = {A Counterexample to the Possibility of an Extension of the {Eckart-Young} Low-rank Approximation Theorem for the Orthogonal Rank Tensor Decomposition},
journal = {SIAM Journal on Matrix Analysis and Applications},
volume = {24},
number = {3},
pages = {762--767},
month = {January},
year = {2003},
doi = {10.1137/S0895479801394465},
}