By generating an eigen-beam by the principal eigenvector of the transmit correlation matrix of own desired channel, the proposed scheme can provide the achievable sum-rate comparable to the full channel information-based minimum mean square error beamforming scheme in correlated channel environments. ...
terms of the scaling (shrinkage or expansion) along each eigenvector of the predictor correlationmatrix of this paper is to convey some new theoretical results concerning the shrinkage structureof PLS xip), where i 1, 2, , n. Here, we assume n > p; with some minor modifications Krylov...
For the reconstructed multiplex network encoded by the expectation E[Q(M)], we binarize the matrix E[Q(M)] and randomly remove nodes in one layer with probability 1 − p (see Supplementary Note 4 for more details of the process). We calculate the size of GMCC (giant mutually ...
Calculate the main eigenvector of qh, Ah ‘ah. Wh is GhAhqh, wh = wh / | | wh | wh |, and wh as the column vector of W. Ph = Mhwh, ch = wh ‘Mhwh, ph = ph/ch, and ph is the column vector of P. Qh = Ah ‘wh/ch, and qh as the column vector of Q. Ah + ...
ρTA = ,, a2 abeiϕ 0 0be−iϕ b2 be−iϕg ag beiϕg g2 0 ag 0 0 ,,, . (12)The partially transposed matrixρTA is a negative matrix with a negative eigenvalueλ−=−ag and the corresponding eigenvector ,Ψ−G,= (a+g)4ag+2 |100,− beiϕ4ag+2 |000...
Calculate the principal eigenvector of qh and Ah ‘ah. Wh = Ahqh, ch = wh ‘mhwh, wh = wh/SQRT (ch), and wh as the column vector of W. The ph is the Mhwh, and the ph is the column vector of P. Qh = Ah ‘wh and Q h as the column vector of Q. The vh = Chph, ...
It can be proved that eigenvector of (I − β1W − β2I) −1 is 1, and the corresponding eigenvalue is (1 − β1 − β2) −1, where 1=(1, ⋯, 1) T with matching dimensions. Then (I − β1W − β2I) −11=(1 − β1 − β2) −11....
Each averaged error operator Λn¯ is characterized by a triple of numbers, which can be combined into a vector fn≡(anbncn), (17) and Eq. (16) is a linear relation between fn+1 and fn, which we describe by an iteration matrix M: fn+1=M^fn. (18) Clearly, the n-dependence...
This overall pattern can be represented by a response vector or a response matrix. In our modeling we have used the aggregate index, De as the response vector. In the PLS-VIP analysis, the number of indicators is reduced in a way such that variations in the set of reduced indicators are...
(μ) and the minimum eigenvalue (λmin)124of the data covariance matrix of the input signal. From the received signals and data, the MISO PZF adaptive algorithm518may generate the overall parameter vector f512including the parameters f1512(1), f2512(2), . . . fp512(p) of the filters...