edmcr (version 0.2.0)

gram2edm: Linear Matrix Operator

Description

gram2edm Inverse Operator of edm2gram

Usage

gram2edm(B)

Arguments

B

A centered, positive semi-definite matrix.

Value

D A matrix in \(D_{n}^{-}\). If the input matrix B is a gram matrix, D is a Euclidean Distance Matrix.

Details

The edm2gram function performs the following transformation:

$$edm2gram(D_{n}^{-}) = B_{n}^{+}$$

where \(D_{n}^{-}\) is the space of symmetric, hollow matrices, negative definite on the space spanned by \(x'e = 0\) and \(B_{n}^{+}\) is the space of centered positive definite matrices.

The gram2edm function performs the inverse operation, taking a matrix in \(B_{n}^{+}\) and transforming it to a matrix in \(D_{n}^{-}\).

$$gram2edm(B_{n}^{+}) = D_{n}^{-}$$

Therfore, gram2edm on \(B_{n}^{+}\) is the inverse operator of edm2gram on \(D_{n}^{-}\).

See Also

edm2gram

Examples

# NOT RUN {
 
X <- cbind(runif(100,0,1),runif(100,0,1))
G <- X %*% t(X)
gram2edm(G)

# }