2008/02/17 by Pierre Comon, P. Comon, Comon, P. +2
Computer Science · Engineering · Mathematics · #Advanced MIMO Systems Optimization #F.1.3 #FOS: Computer and information sciences #G.0 #G.3 #I.1 #J.2 #Mathematical Software (cs.MS) #Other Computer Science (cs.OH) #Tensor decomposition and applications #Wireless Communication Networks Research #cs.MS #cs.OH
paper · pdf · doi:10.48550/arxiv.0802.2371
arxiv created 2008/02/17 · openalex publication_date 2008/02/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The concept of tensor rank, introduced in the twenties, has been popularized at the beginning of the seventies. This has allowed to carry out Factor Analysis on arrays with more than two indices. The generic rank may be seen as an upper bound to the number of factors that can be extracted from a given tensor. We explain in this short paper how to obtain numerically the generic rank of tensors of arbitrary dimensions, and compare it with the rare algebraic results already known at order three. In particular, we examine the cases of symmetric tensors, tensors with symmetric matrix slices, or tensors with free entries.