# subspaceDistance

##### Distance Between Linear Spaces

Evaluate the distance between two linear subspaces using the measure proposed by Li, Zha and Chiaromonte (2005).

- Keywords
- multivariate, algebra

##### Usage

`subspaceDistance(B0, B1)`

##### Arguments

- B0
Matrix whose columns are a basis for the first subspace.

- B1
Matrix whose columns are a basis for the second subspace.

##### Details

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 `B0,B1`

.
This measure of distance was proposed by Li, Zha and Chiaromonte
(2005). See also Xia (2007).

##### Value

A single numeric value.

##### References

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.

*Documentation reproduced from package spatstat, version 1.52-1, License: GPL (>= 2)*