Sentence examples for entry given by from inspiring English sources

We denote as the unitary FFT matrix with its th entry given by: (16).

Henceforth (xotimes x) denotes the matrix in (mathbb {S}^N) with the (i, j) entry given by (x_ix_j) for (xin mathbb {R}^N).

where u is a unitary matrix and Σ = diag{λ1,......,λMtMr} is a diagonal matrix with each diagonal entry given by a eigenvalue.

where. is the mutual impedance matrix at the receiver side, and is a diagonal matrix with its th entry given by,. is given by It is noted that the approximate conjugate match [12] is also assumed at the receiver side, so that the load impedance matrix is diagonal with its entry given by, for.

Let A be the n×n diagonal matrix with the ith entry given by ({r_{i}^{2}} 1-h_{textit {ii} 1-h_{textitit {ii}}}), where r i is the ith residual based on the ordinary least squares estimator.

where Λt and Λc are, respectively, the diagonal matrices with each diagonal entry given by a real and nonnegative eigenvalue of and, Q is the unitary eigenvector matrix of and, and μ is a scalar constant that satisfies the transmitted power constraints.

where H ( u ) = F h circ ( u ) F - 1 is the diagonal channel matrix of user u with the diagonal (k,k -entry given by H k,k -entry1 N p ∑ m = 0 L h - 1 h m ( u ) e - j 2 πmk / N p, (5).

Thus, the resulting Hessian is a diagonal matrix with diagonal entries given by (27).

Let (widetilde {mathbf {C}}) be the J×J matrix with entries given by [widetilde{mathbf{C}}]_{ell,m}=frac{ -1)^{ell+m}c^{(ell,m}=frac{ -1}.

Under this assumption, the matrix D is a diagonal matrix with only L non-zero entries given by diag (D) = [p1 ⋯ p G ] T = p, being p ∈ ℝ + G × 1.

Typically, the measurement error component is also assumed to be normally distributed with constant variance, i.e. U ~ N P (0, ∑), where is ∑ a diagonal matrix with the main diagonal entries given by, for p = 1,..., P.