ELA, Volume 10, pp. 201-211, July 2003, abstract.

Optimal Subspaces and Constrained Principal 
Component Analysis

Jean-Daniel Rolle

The main result of this article allows formulas 
of analytic geometry to be elegantly unified, 
by readily providing parametric as well as cartesian
systems of equations. These systems characterize 
affine subspaces in R^p passing through specified 
affine subspaces of lower dimension. The problem 
solved is closely related to constrained principal 
component analysis. A few interesting applications 
are pointed out, notably a measure of the relative 
loss of optimality due to the constraints. The results 
pave the way for further research.