edmcr (version 0.2.0)

edm2psd: Linear Matrix Operator

Description

edm2psd Convert an Euclidean Distance Matrix to a Positive Semi-definite Matrix

Usage

edm2psd(D, V = NULL)

Arguments

D

A matrix in the set D_n^-.

V

A projection matrix satisfying V'1 = 0 and VV' = I

Value

S A symmetric, positive semi-definite matrix

Details

For a matrix D in \(D_{n}^{-}\), edm2psd will be in the space of positive semi-definite matrices. Therefore, if D also has zero diagonal, we have the following property:

D is a Euclidean Distance Matrix if and only if edm2psd is positive semi-definite.

This operator gives us another method to characterize the existence of a Euclidean distance matrix.

See Also

psd2edm edm2gram

Examples

# NOT RUN {
XY <- cbind(runif(100,0,1),runif(100,0,1))
D <- dist(XY)
edm2psd(as.matrix(D))

# }