Approximate decomposability in and the canonical decomposition of 3-vectors

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