This paper explores some properties of the quadratic subspace, a tool for dimension reduction in discriminant analysis (Velilla, 2008, 2010). This linear manifold has a fairly complex structure, and it may sometimes include components with both mean and covariance separation properties. In this case, an assumption of orthogonality between the leading location directions and the bulk of the dispersion subspaces can help to find an adequate directional representation of it in practice. Two real data sets are analyzed. © 2012 Elsevier B.V.
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