# orthogonalInSubspace -- Orthogonal of a space

## Synopsis

• Usage:
S = orthogonalInSubspace(D, T, tol)
• Inputs:
• D, an instance of the type DualSpace, or an instance of the type PolySpace a space of which to find the orthogonal
• T, an instance of the type PolySpace, ambient space
• tol, , a positive number, the numerical tolerance
• Outputs:

## Description

This functions computes the subspace of the polynomial space T that is orthogonal to the dual space (or polynomial space) D.

 i1 : R = CC[x,y]; i2 : T = polySpace matrix{{1,x,y}}; i3 : D = dualSpace(matrix{{x-y}}, origin R); i4 : S = orthogonalInSubspace(D, T, 1e-6) o4 = | 1x+y 1 | o4 : PolySpace

## Ways to use orthogonalInSubspace :

• "orthogonalInSubspace(DualSpace,PolySpace,Number)"
• "orthogonalInSubspace(PolySpace,PolySpace,Number)"

## For the programmer

The object orthogonalInSubspace is .