Distance Between Linear Spaces
Evaluate the distance between two linear subspaces using the measure proposed by Li, Zha and Chiaromonte (2005).
Matrix whose columns are a basis for the first subspace.
Matrix whose columns are a basis for the second subspace.
This algorithm calculates the maximum absolute value of the
eigenvalues of \(P1-P0\) where \(P0,P1\) are the projection
matrices onto the subspaces generated by
This measure of distance was proposed by Li, Zha and Chiaromonte
(2005). See also Xia (2007).
A single numeric value.
Guan, Y. and Wang, H. (2010) Sufficient dimension reduction for spatial point processes directed by Gaussian random fields. Journal of the Royal Statistical Society, Series B, 72, 367--387.
Li, B., Zha, H. and Chiaromonte, F. (2005) Contour regression: a general approach to dimension reduction. Annals of Statistics 33, 1580--1616.
Xia, Y. (2007) A constructive approach to the estimation of dimension reduction directions. Annals of Statistics 35, 2654--2690.