subspace: The distance between two subspaces.

In TRES: Tensor Regression with Envelope Structure

Description

This function calculates the distance between the two subspaces with equal dimensions span(A) and span(B), where A \in R^{p\times u} and B \in R^{p\times u} are the basis matrices of two subspaces. The distance is defined as

\|P_{A} - P_{B}\|_F/√{2d},

where P is the projection matrix onto the given subspace with the standard inner product, and d is the common dimension.

Usage

subspace(A, B)

Arguments

A	A p-by-u full column rank matrix.
B	A p-by-u full column rank matrix.

Value

Returns a distance metric that is between 0 and 1

TRES documentation built on Oct. 20, 2021, 9:06 a.m.