Sentence examples for has singular value from inspiring English sources

([36]) Given a matrix (F in {mathbb R}^{m times N}), N≥m, suppose F has singular value decomposition UΣV ∗.

The motivating problem is to find sufficient conditions on a symbol which ensure that the corresponding operator has singular values with a prescribed rate of decay.

Consider SVD of a given matrix A, A have singular value decomposition A=UvarSigma {V}^{mathrm{T}} (6).

Starting with the sentiment time series for each book (b_{i}) as row i in the matrix A, we apply the SVD to find A = U Sigma V^{T} = W V^{T}, (1) where U contains the projection of each sentiment time series onto each of the right singular vectors (rows of (V^{T}), eigenvectors of (A^{T}A)), which have singular values given along the diagonal of Σ, with (W = U Sigma).

Typically, a selection is made by inspecting the fall-off of singular values of the most significant components, rejecting higher components having singular values that are in excess of a linear trend for the most significant components.

Our study also has singular strengths.

Since is of rank w.p.1, it has the singular value decomposition, where is a diagonal matrix whose diagonal elements are the positive singular values of.

According to Lemma 2 and the observation that the effective channel of Equation 5 is the receive antenna correlation matrix (textbf {R}_{r_{k}}), we have the singular value matrix of (phantom {dot {i}!}textbf {R}_{r_{k}}) as (phantom {dot {i}!}mathbf {Lambda }_{k}=lbrack 1+ rho _{r_{k}}, ; 0 ; 0, ; 1-rho _{r_{k}} rbrack ) when each user node has two receive antennas.

Note, however, that the condition of having a singular value larger than one and thus the loss of robustness does not necessarily mean that the system must behave in an unstable manner.

Some authors have used singular value decompositions to regularize the regression models [ 28- 30].

If is decomposed by SVD, has nonzero singular values at most.