Approximate decomposability in and the canonical decomposition of 3-vectors

Leventides, J. & Karcanias, N. (2016). Approximate decomposability in and the canonical decomposition of 3-vectors. Linear and Multilinear Algebra, doi: 10.1080/03081087.2016.1158230

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Given a (Figure presented.)3-vector (Formula presented.) the least distance problem from the Grassmann variety (Formula presented.) is considered. The solution of this problem is related to a decomposition of (Formula presented.) into a sum of at most five decomposable orthogonal 3-vectors in (Formula presented.). This decomposition implies a certain canonical structure for the Grassmann matrix which is a special matrix related to the decomposability properties of (Formula presented.). This special structure implies the reduction of the problem to a considerably lower dimension tensor space ⊗3R2 where the reduced least distance problem can be solved efficiently.

Item Type: Article
Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis in Linear and Multilinear Algebra on 6 Apr 2016, available online:
Uncontrolled Keywords: exterior algebra, decomposability, best decomposable approximation, Grassmann variety
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences > Engineering

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