Abstract

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.

Publication 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: http://www.tandfonline.com/10.1080/03081087.2016.1158230
Publisher Keywords:	exterior algebra, decomposability, best decomposable approximation, Grassmann variety
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Engineering

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