# subspaceDistance

0th

Percentile

##### 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.

##### Aliases
• subspaceDistance
Documentation reproduced from package spatstat, version 1.55-1, License: GPL (>= 2)

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