Therefore, the potential parallelism in solving the lower and upper triangular matrices in the

null space algorithm increases of one order of magnitude from the two dimensional to the three dimensional case.

If we find a fundamental cycle basis to the graph of the incidence matrix S we can easily extend it to the

null space basis of [(B C).sup.T].

Since we have illustrated the basic principle in the context of the

null space problem, we omit further numerical calculations.

Such user selection methodology is based on an iterative

null space projection (NSP) and it achieves the best suboptimal solution to the problem (11) for a class-B algorithm regardless of the coding scheme, which will be elaborated upon in the following sections.

Recall that, [I.sup.p] is the

null space of the semi-norm; hence it is obviously closed in [M.sup.p].

Thus [V.sub.k] should lie in the

null space of [[bar.H].sub.k,M], i.e., [V.sub.k] [subset] null([[bar.H].sub.k,M]), where [[bar.H].sub.k,M] is defined as

The

null space of N corresponds to all linear combinations of the basis in (3.13) that result in real vectors.

Thirdly, we also compare the performance of our two proposed schemes with the

null space based beamforming scheme.

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

null space of B, [{[x.sub.i]}.sup.r.sub.i=1] a basis of the

null space of F, and [{[y.sub.i]}.sup.m-r.sub.i=1] it a set of linearly independent vectors that complete null(F) [union] null(B) to a basis of [r.sup.n].

sparse column space basis, sparse

null space basis, block angular matrix, block diagonal matrix, matching, hypergraph partitioning, inverse of a basis

The

null space of the discrete (curl, curl) operator has dimension [N.sub.nodes-1] and is spanned by [T.sup.3].

Since the size of the matrix F is 3d x 4d, G can be chosen as d basis vectors of the

null space of F, from which [[??].sub.1] and [[??].sub.2] can be acquired at Rx 4.

This is true as the TR-MUSIC employs the

null space of the multi-static data matrix (MDM) of the system.

In this inexact BDDC,

null space corrections are not necessary.

In Section 3, we present a block Hankel matrix, related data estimation equations, and deletion of input items based on

null space projection for subspace model identification process.