Orthogonal tensor decompositions

[摘要] 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].

[发布日期] 2000-03-01 [发布机构] Sandia National Laboratories

[关键词] Orthogonal Transformations;Tensors;Matrices;Mathematics;99 General And Miscellaneous//Mathematics, Computing, And Information Science