Approximate decomposability in and the canonical decomposition of 3-vectors

Given a 3-vector the least distance problem from the Grassmann variety is considered. The solution of this problem is related to a decomposition of into a sum of at most five decomposable orthogonal 3-vectors in . This decomposition implies a certain canonical structure for the Grassmann matrix whic...

Full description

Saved in:
Bibliographic Details
Published in:Linear & multilinear algebra 2016-12, Vol.64 (12), p.2378-2405
Main Authors: Leventides, John, Karcanias, Nicos
Format: Article
Language:English
Subjects:
Algebra
best decomposable approximation
decomposability
Decomposition
exterior algebra
Grassmann variety
Mathematical analysis
Reduction
Tensors
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Given a 3-vector the least distance problem from the Grassmann variety is considered. The solution of this problem is related to a decomposition of into a sum of at most five decomposable orthogonal 3-vectors in . This decomposition implies a certain canonical structure for the Grassmann matrix which is a special matrix related to the decomposability properties of . This special structure implies the reduction of the problem to a considerably lower dimension tensor space ⊗ 3 R 2 where the reduced least distance problem can be solved efficiently.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2016.1158230