Sentence examples for be the singular values from inspiring English sources

Let λ i and γ i be the singular values of H and (tilde {mathbf {W}}), respectively, both in non-increasing order, i.e., λ 1≥⋯≥λ r ≥0 and γ 1≥⋯≥γ r ≥⋯≥γ K ≥0.

Let (sigma_{1}(A)geqcdotsgeqsigma_{ncdotsgeqsigma_{n}(A)), (sigma _{1}(B) geqsigma_{2}(B) geqcdotsgeqsigma_{n}(B)) and (sigma_{1} A-B) geqsigma_{2}(A-B) geqcdotsgeqsigma_{n}(A-B)) be the singular values of the complex matrices (A=(a_{ij})), (B=(b_{ij})) and (A-B), respectively.

Let (s_{1}geq s_{2} geqcdotsgeq s_{n}) and (delta_{1}geqdelta_{2} geq cdotsgeqdelta_{n}) be the singular values of the complex matrices (A=(a_{ij}) inmathbb{C}^{ntimes n}) and (B=(b_{ij}) inmathbb{C}^{ntimes n}), respectively.

Let be the singular value decomposition of the data.

Let (Sigma= UAV^{H} ) be the singular value decomposition of the matrix A with order n.

The optimal decoding matrix U and encoding matrix V should be the singular value decomposition (SVD) of H.

More particularly, let R=USV T be the singular value decomposition of the obtained Gram matrix, after rank reduction and normalization.

where λi and r are the singular values and the rank of B H CB, respectively.

λ i j 1 ∕ 2 being the singular values of H i V ˜ i ( 0 ).

where σ j (A),j = 1,…,N are the singular values of A. The following lemmas will be useful later.

Considering that and are orthogonal bases for subspaces and, respectively, the canonical correlations are the singular values of.