dual {gellipsoid}

Dual or 'Inverse' of an ellipsoid

Description

dual produces the orthogonal complement for subspaces or for ellipsoids. This is equivalent to inverting \Sigma or an inner product ip when these are non-singular.

Usage

dual(x, ...)

## S3 method for class 'gell'
dual(x, ...)

Arguments

x

An object, of class "gell"

...

Other arguments, unused for now.

Details

At present, dual is only defined for objects of class "gell".

In the (U,D) representation, the dual simply has the columns of U in the reverse order, and the reciprocals of the diagonal elements of D, also in reverse order.

Value

A (U, D) representation of the dual, with components LIST, use

u

Right singular vectors

d

Singular values

Author(s)

Georges Monette

References

Dempster, A. (1969). Elements of Continuous Multivariate Analysis Reading, MA: Addison-Wesley.

See Also

gell

Examples

(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 )