distrMod (version 2.1.1)

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)

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).

Value

• logical

concept

• pseudo inverse
• projector
• ker

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))
isKerAinKerB(D,ma)
isKerAinKerB(ma,D)