(7), [V.sup.N] spans the

nullspace of H and is the orthogonal complement of [V.sup.S].

where [J.sup.+] is the pseudoinverse of J, [P.sup.[perpendicular to]] (J) is the projection operator which projects arbitrary joint rates into the

nullspace of the end-effector's Cartesian coordinates, and [xi] is an arbitrary joint rate vector.

The normalized eigen vectors corresponding to the zero eigen values of [S.sub.NC.sup.i[phi]] form a basis of the

nullspace of [S.sub.NC.sup.i[phi]].

GRATEFUL MED users often get no retrieval because of "ANDing into

nullspace," using terminology seldom employed in indexing, using terms too specific or not specific enough, using MeSH specialty headings inappropriately, and by using stop words.

The dimension of the eigenvalue [lambda] =1 is n + [n.sub.0], where [n.sub.0] is the dimension of the nontrivial

nullspace of [B.sub.1] + [B.sub.2].

The Laplacian matrix is singular with a

nullspace dimension of one (because the pruned graph is connected).

Given a(n) and b(n) in (14), the ICI reconstructing vector [v.sup.H.sub.1(n)] is determined by the left-hand

nullspace of the matrix [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

and we are only looking for eigenvectors in the

nullspace of [U.sup.*.sub.2]M.

We note at this point that this matrix is in general singular, as it is well known that the vector of ones is a member of the

nullspace of [B.sup.T] (see [6, Chapter 5] for instance)--the matrix in (3.1) therefore has two zero eigenvalues (one corresponding to each appearance of [B.sup.T]).

However, since [[bar.H.]sub.l] [member of] [R.sup.4 x 4] is a square matrix with full rank, its

nullspace, which is also the intersection subspace of span([[??].sub.i]) and span([[??].sub.j]).

where F [member of] [R.sup.nxk] is a matrix the columns of which form an orthonormal basis of the

nullspace of L; cf.

A is a matrix, [a.sup.m] is a mth column vector of A, [A.sup.H] denotes the conjugate transpose of A, and [parallel]A[[parallel].sub.F] is its Frobenius norm; tr(A) is its trace, span (A) is its column space, null(A) returns

nullspace vectors of column space of A, eig(A) is any eigenvector of A, O(A) consists of the orthonormal basis vectors that span the column space of A; [I.sub.M] is the M x M identity matrix; [C.sup.M] is the M-dimensional complex vector space.

By using an orthogonal projection P whose

nullspace is Z the Krylov space solver is then applied only to the orthogonal complement [Z.sup.[perpendicular to]] by restricting the operator A accordingly.

where [[phi].sub.ij] [member of] [0,1] are uniformly distributed random numbers, [OMEGA] = {1, ..., n}x{l, ..., m}, [summation] = {1, ..., l} x {1, ..., m} and l >> n, such that [bar.K] has a large

nullspace. Furthermore, we consider f instead of g, with f being corrupted by Poisson noise.