distrMod (version 2.9.4)

isKerAinKerB: 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)

Value

logical

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).

Author

Peter Ruckdeschel

Details

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

Examples

ma <- cbind(1,1,c(1,1,7))
D <- t(ma %*% c(0,1,-1))
## IGNORE_RDIFF_BEGIN
## note that results may vary according to BLAS
isKerAinKerB(D,ma)
isKerAinKerB(ma,D)
## IGNORE_RDIFF_END