orthogonal complement


Also found in: Wikipedia.

orthogonal complement

[ȯr′thäg·ən·əl ′käm·plə·mənt]
(mathematics)
In an inner product space, the orthogonal complement of a vectorvconsists of all vectors orthogonal tov; the orthogonal complement of a subset S consists of all vectors orthogonal to each vector in S.
References in periodicals archive ?
They define a normal tractor bundle in the ambient standard tractor bundle along the submanifolds, and show that the orthogonal complement of this bundle is not canonically isomorphic to the standard tractor bundle of the submanifold.
Orthogonal complement: Given a subspace W of a scalar product space V, the set of all vectors orthogonal to W is the orthogonal complement, [W.sup.[perpendicular to]] of W:
When using ZF, the multiuser interference is totally cancelled out by projecting every stream onto the orthogonal complement of the inter-user interference (Larsson et al., 2014).
In the process of algorithm implementation, SVD should be applied twice to solve the orthogonal complement space in the two methods.
Since e(V') = e(V)e([V.sup.[perpendicular to]]), where [V.sup.[perpendicular to]] is the orthogonal complement of V in V', we see that e(V) also divides e(W).
is an orthogonal complement of the component (25) to the full vector (and does not contain 0-component).
For any nonempty subset A of [V.sub.s], we denote [A.sup.[perpendicular to]] as the orthogonal complement of A in V; that is,
Since the capacity-achieving USTM signal distribution at high SNR is isotropic on the Grassmannian manifold [G.sub.T,M] and each signal point is denoted as a unitary matrix [PHI], [bar.[PHI]] is defined as an antipodal point of [PHI] if [bar.[PHI]] is the orthogonal complement of [PHI] on [G.sub.T,M].
Since [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] converges to the orthogonal complement N of L in [T.sub.[sigma]]M.
The common column space is the orthogonal complement of the column space of [U.sub.1].
In connection with the above Krylov subspace methods, Reichel and his collaborators [1, 2, 3, 6] therefore proposed to decompose the solution into a component in [W.sub.p] and another component in the orthogonal complement [W.sup.[perpendicular to].sub.p], which leads to the idea of augmented Krylov subspace methods; see also [17].

Full browser ?