These algorithms build the nested dissection structure of [[??].sub.22] and the

null space matrix Z.

This means that the components of

null space vectors corresponding to faces with Neumann boundary conditions must be zero.

The function 1 is also in the

null space of I + [K.sup.*], the adjoint of the integral operator in (6.1), which is clearly necessary for solvability.

The metric for user selection is based on the channel component projected onto the

null space of the space spanned by the previously selected user channels.

The quotient of [M.sup.p] with respect to the

null space [I.sup.p] of the semi-norm is therefore a Banach space, which we denote by [[??].sup.p].

If [alpha] is a

null space curve with a spacelike principal normal [??], then the following Frenet formulas hold

[(A).sup.T], [(A).sup.H], [parallel]A[parallel][sub.2], span (A), null (A) and [A.sup.[dagger]] = [A.sup.H] [([AA.sup.H]).sup.-1] indicate transpose, Hermitian, the Frobenius norm, the column space, the

null space and the Moore-Penrose inverse matrix of A, respectively.

Assume now that a basis for the

null space of H is given by the vectors

Secondly, with the assumption that the eavesdropper's Channel State Information (CSI) is known at the transmitters, the authors in [7] designed the relay beamforming vector in the

null space of the eavesdropper's channel to eliminate the information leakage to the eavesdropper.

Let [{[z.sub.i]}.sup.n-m.sub.i=1] be a basis of the

null space of B.

This paper presents a new combinatorial approach towards constructing a sparse, implicit basis for the

null space of a sparse, under-determined matrix A.

First, even if these inclusions hold, the

null space [Z.sub.h] is not necessarily a subspace of Z and so (4.7) does not follow from (2.8).