isKerAinKerB {distrMod}R Documentation

isKerAinKerB

Description

For two matrices A and B checks whether the null space of A is a subspace of the null space of B, in other words, if Ax=0 entails Bx=0.

Usage

isKerAinKerB(A, B, tol = .Machine$double.eps)

Arguments

A a matrix; if A is a vector, A is coerced to a matrix by as.matrix.
B a matrix; if B is a vector, B is coerced to a matrix by as.matrix.
tol the tolerance for detecting linear dependencies in the columns of a and up to which the two projectors are seen as equal (see below).

Details

via calls to svd, the projectors pi_A and pi_B onto the respective orthogonal complements of ker(A) and ker(B) are calculated and then is checked whether pi_B pi_A = pi_B.

Value

logical

Author(s)

Peter Ruckdeschel Peter.Ruckdeschel@itwm.fraunhofer.de

Examples

ma <- cbind(1,1,c(1,1,7))
D <- t(ma %*% c(0,1,-1))
isKerAinKerB(D,ma)
isKerAinKerB(ma,D)

[Package distrMod version 2.0.7 Index]