orthogonal complement


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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 ?
p] and another component in the orthogonal complement [W.
The basis generated by this approach corresponds to a Krylov subspace limited to the orthogonal complement of [V.
The center of the inversion hyperplane arrangement I (w) is the orthogonal complement of [V.
U], or equivalently is the subgroup of W which acts identically on the orthogonal complement of U in V.
perpendicular to]], which represents the orthogonal complement of the tangent vector field of the curve.
Analogously, osculating curves in the Minkowski space-time are defined in [6] as the space curves whose position vector (with respect to some chosen origin) always lies in its osculating space, which represents the orthogonal complement of the first binormal or second binormal vector field of the curve.
The over-identifying restriction imposed by Lee [1995] is on the orthogonal complement to the error correction coefficients, which is equivalent to restricting the error correction coefficients themselves.
1) is the total impact matrix from the AR representation of equation (8)(10) and the pxk matrices [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are the orthogonal complements to the matrix of error correction coefficients, [Alpha], and the matrix of cointegration vectors, [Beta], respectively (i.
By using an orthogonal projection P whose nullspace is Z the Krylov space solver is then applied only to the orthogonal complement [Z.
H] = P; so, Q is the orthogonal projection onto Z, while P is the orthogonal projection onto the orthogonal complement [Z.
Therefore, it is inexpensive to compute a sparse interpolation matrix Q that completely spans the orthogonal complement to Range(Z) containing all eigenvectors not in the columns of Z.
Let Z be a collection of LSEVs of L that have been identified and let Q be a sparse matrix that spans the orthogonal complement of Z.

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