Sentence examples for singular value for from inspiring English sources

As an application, we consider the left and right singular vectors associated with the largest singular value for complex Toeplitz matrices.

Recently, many people focus on bounding the largest singular value for nonnegative rectangular tensors [6, 9, 10].

In this test, we have difficulties in computing the largest singular value for ill-conditioned matrices (A) and (B).

In this paper, a new S-type upper bound (Psi^{S}(mathcal{A})) of the largest singular value for a nonnegative rectangular tensor (mathcal {A}) with (m=n) is obtained by breaking N into disjoint subsets S and its complement.

For the second issue, suppose conventional SVD of an arbitrary constant matrix A. If the pair u → and v → are the left and right singular vectors corresponding to a non-zero singular value, for an arbitrary scalar phase angle θ, the pair e j θ u → and e j θ v → are also left and right singular vectors corresponding to the same singular value.

The singular value for this significant LV accounted for 64.5% of cross-block covariance.

This transformation can be extended to the tensor case where the forward-backward averaged data tensor is replaced by a real-valued data tensor possessing the same r-mode singular values for all r = 1, 2,..., R + 1 (see [19] for details).

We study the distribution of singular values for the matrix of regression coefficients and for the matrix of predicted responses.

The placement criterion is based on a previously defined concept called control reconfigurability, which imposes a requirement on the minimum Hankel singular values for all anticipated fault scenarios.

It is obtained that the eigenvalues are equal to the corresponding singular values for the symmetric system, the singular values are equal to the products of the unit imaginary number and corresponding eigenvalues for the anti-symmetric system, and the differences of the eigenvalues and corresponding singular values for the asymmetric system depend on the anti-symmetric stiffness.

The definition of singular values for tensors was first introduced in [7].