Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4602444 | Linear Algebra and its Applications | 2009 | 13 Pages |
Abstract
Let MM be a matrix of order n=pqn=pq. Then the tensor rank of MM is defined as the minimal possible ρρ in expressions of the form M=∑t=1ρUt⊗Vt, where UtUt and VtVt are matrices of order pp and qq, respectively. Let MM be a nonsingular matrix of tensor rank 3 and, moreover, of the formM=I+A⊗X+Y⊗BM=I+A⊗X+Y⊗Bwith rankX=rankY=1. Then, it is discovered and proved that the tensor rank of M-1M-1 is bounded from above by 5 independently of pp and qq, the estimate being sharp. Some related and extended results are also given.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Ivan Oseledets, Eugene Tyrtyshnikov, Nickolai Zamarashkin,