Sentence examples for matrix of singular from inspiring English sources

Thus, is a diagonal matrix of singular values while and are square and unitary matrices.

Next, consider the singular value decomposition (SVD) of, where and are unitary matrices and is a diagonal matrix of singular values of.

The filter matrix is given by T = Θ − 1 2 U T with Θ and U being the diagonal matrix of singular values and the matrix of singular vectors of the covariance matrix C x x = E [ x x T ], respectively[3, 12].

Let the singular-value decomposition of H ^ as follows: H ^  =  U Σ V H (19). where U and V are unitary matrixes and Σ is a diagonal matrix of singular values σ ′ i.

The singular value decomposition of a matrix A with size m × n is given by A=UD{V}^T, (6 where U and V are orthogonal matrices, and D = diag(λ i ) is a diagonal matrix of singular values λ i, i = 1, 2, ⋯, which are arranged in decreasing order.

Since the available matrix of singular vectors at each frequency is U ′[k], inserting (9) in (18) for each singular vector separately leads to ∑ k = 0 K − 1 u i ′ [ k ] e − j θ i u [ k ] w K − kn = 0 (19).

The core tensor W and mode matrices U n 's correspond to the matrices of singular values and orthonormal basis vectors in matrix SVD, respectively.

We can introduce a regularization by applying the singular value decomposition to Z as Z ≈ U qD qV q T, where D q is a diagonal matrix of q singular values, and U q and V q are matrices of singular vectors associated with the q singular values.

3: Compute the Singular Value Composition (SVD) of, and let be the matrix of left singular vectors corresponding to the m largest singular values.

where Ũ i and ( {tilde{boldsymbol{Lambda}}}_i ) denote the left singular vector matrix and the matrix of ordered singular values of ( {tilde{mathbf{H}}}_i ), respectively.

We then construct a nonlinear eigenvalue problem in the matrix form for given azimuthal wavenumbers and compute the eigenfrequencies and their conjugate mode shapes through solving a determinantal equation followed by evaluating the adjoint matrix of a singular linear map.