signature {gellipsoid}

Signature of a Generalized Ellipsoid

Description

Calculates the signature of a generalized ellipsoid, a vector of length 3 giving the number of positive, zero and infinite singular values in the (U, D) representation

Usage

signature(G)

Arguments

G

A class "gell" objects

Value

A vector of length 3, with named components pos, zero and inf

Author(s)

Georges Monette

References

Friendly, M., Monette, G. and Fox, J. (2013). Elliptical Insights: Understanding Statistical Methods through Elliptical Geometry. Statistical Science, 28(1), 1-39.

See Also

isBounded

Examples

(zsph <- gell(Sigma = diag(3)))  # unit sphere in R^3

(zplane <- gell(span = diag(3)[,1:2]))  # a plane

dual(zplane)  # line orthogonal to that plane

(zhplane <- gell(center = c(0,0,2), span = diag(3)[,1:2]))  # a hyperplane

dual(zhplane) # orthogonal line through same center (note that the 'gell'
              # object with a center contains more information than the geometric plane)

zorigin <- gell(span = cbind(c(0,0,0)))
dual( zorigin )

# signatures of these ellipsoids
signature(zsph)
signature(zhplane)
signature(dual(zhplane))