null space

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a space that contains no points

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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.
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