Sentence examples for basis of the null from inspiring English sources

The orthonormal basis of the null space of W denoted as N W ∈ ℂ N × ( N − K ( K − 2 ) ) here can be obtained by the singular value decomposition: W = S W N W Λ W V W H. (15).

Furthermore, we model the orthogonal basis of the null space of ({mathbf {B}}_{1}^{ast } ) as ({{mathbf {N}}_{1}} in {mathbb {C}^{N times left ({N - {r_{1}}} right)}}), and ({{boldsymbol {pi }}_{1,n}} in {mathbb {C}^{N times 1}}, 1 le n le N - {r_{1}}) as the nth column of N 1.

Mathematically, EMs form the convex basis of the null space solution of a metabolic network stoichiometric matrix.

This matrix was used as the basis of the null model for the transformed allele frequencies at each SNP to be tested.

During the identification of the basis of the null space, only the set of reactions whose fluxes hit the bounds during FVA were used to decrease processing time.

A subset of zero-flux reactions can be detected by analyzing the basis of the null space to ensure that each row has at least one non-zero entry [ 20].

(x_) is the solution of problem (1), which satisfies the strong second-order sufficient condition, that is, let the columns of (Z_) denote an orthogonal basis for the null space of ([ begin{matrix} A & -D^{frac{1}{2}}_ end{matrix} ] ), then there exists (varpi>0) such that d^{T}({Z_M_{f_{Z_ d geqslantvarpi Vert d Vert ^{2}, quad forall d. (33).

Here, we choose for the k th cell site the d k columns of Fk,L to be an orthonormal basis for the null space of A k = H 1 k ' ⋯ H k − k ' | H k + k ' ⋯ H Kk ' ', if 1 < k < K A k = H k + k ' ⋯ H Kk ' ', if k = 1 A k = H 1 k ' ⋯ H k − k ' ', if k = K (3).

Indeed, a well known result of linear algebra implies that, where, κ 0 is a J × 1 vector that satisfies is a J × d matrix whose columns form a basis for the null space of matrix, and ℜ d is the space of all d × 1 real valued vectors.

Finally, in all previous methods, a basis for the null space of the stoichiometric matrix, i.e., which set of free fluxes is used, needs to be chosen.

Thus, V k (0) is an orthogonal basis for the null space of H ˜ k.