Open AccessOrthogonal tensor decompositions
Author(s) -
Tamara G. Kolda
Publication year - 2000
Publication title -
osti oai (u.s. department of energy office of scientific and technical information)
Language(s) - English
Resource type - Reports
DOI - 10.2172/755101
Subject(s) - orthogonality , counterexample , tensor (intrinsic definition) , mathematics , singular value decomposition , extension (predicate logic) , algebra over a field , linear algebra , decomposition , pure mathematics , tensor product , tensor decomposition , discrete mathematics , computer science , algorithm , geometry , chemistry , programming language , organic chemistry
The authors explore the orthogonal decomposition of tensors (also known as multi-dimensional arrays or n-way arrays) using two different definitions of orthogonality. They present numerous examples to illustrate the difficulties in understanding such decompositions. They conclude with a counterexample to a tensor extension of the Eckart-Young SVD approximation theorem by Leibovici and Sabatier [Linear Algebra Appl. 269(1998):307--329]
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