Path: news.mathworks.com!not-for-mail
From: "Robert Nicholls" <robert.nicholls@comcast.net>
Newsgroups: comp.soft-sys.matlab
Subject: Matlab Subspace Angles
Date: Wed, 9 Jun 2010 21:26:05 +0000 (UTC)
Organization: MIT Lincoln Laboratory
Lines: 6
Message-ID: <hup0td$qr8$1@fred.mathworks.com>
Reply-To: "Robert Nicholls" <robert.nicholls@comcast.net>
NNTP-Posting-Host: webapp-03-blr.mathworks.com
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
X-Trace: fred.mathworks.com 1276118765 27496 172.30.248.38 (9 Jun 2010 21:26:05 GMT)
X-Complaints-To: news@mathworks.com
NNTP-Posting-Date: Wed, 9 Jun 2010 21:26:05 +0000 (UTC)
X-Newsreader: MATLAB Central Newsreader 1915731
Xref: news.mathworks.com comp.soft-sys.matlab:643609

Firstly, I may be off-base but here goes. I believe that if I have a 4 dimensional space (spanned by 4 columns of a 4x4 matrix) then I may have two subspaces defined by the first two columns and the last two columns of the matrix.  The columns may either span the subspaces or define two null spaces. The angle between the two null spaces defined by columns 1:2 and 3:4 should be a two dimensional vector, ie. there are two angles that satisfy the minimization criterion.  The dimension of the angle vector will be defined by the dimension of the subspaces for other sizes of matrix. There are a number of references but Kendall, M.G "A Course in the Geometry of n Dimensions" seems to be straight forward in the definition.   However, the MATLAB subspace function returns a single angle regardless of the dimensions of the subspaces. 

My question then is: What is the single value being returned by the "subspace" function and should it be multidimensional depending on the dimensions of the subspaces (or adjunct spaces)?

Thank,
Bob