Authors
Citation
Tg. Kolda, Orthogonal tensor decompositions, SIAM J MATR, 23(1), 2001, pp. 243-255
Citations number
15
Categorie Soggetti
Mathematics
Journal title
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
ISSN journal
08954798
→ ACNP
Volume
23
Issue
1
Year of publication
2001
Pages
243 - 255
Database
ISI
SICI code
0895-4798(20010418)23:1<243:OTD>2.0.ZU;2-R
Abstract
We explore the orthogonal decomposition of tensors ( also known as multidim
ensional arrays or n-way arrays) using two different definitions of orthogo
nality. We present numerous examples to illustrate the difficulties in unde
rstanding such decompositions. We conclude with a counterexample to a tenso
r extension of the Eckart-Young SVD approximation theorem by Leibovici and
Sabatier [Linear Algebra Appl., 269 (1998), pp. 307-329].