Sentence examples for matrices defined as from inspiring English sources

From (3), it can be noted that the modified precoding matrices defined as V k = W V k IA ∀ k ∈ K, (8).

Here the matrices Q are the scattering matrices defined as Q g g ′ s s ′ = M g g ′ s s ′ exp i s K g s ⋅ d r + s ′ K g ′ s ′ ⋅ d l where s and s′ are + or – signs, g and g′ index the 2D reciprocal lattice vectors, d r and d l are right and left translation vectors, the matrix M is given in equation (11), and a 3 is the primitive unit vector representing the periodicity in the 3rd dimension.

The fitting of the model can be done by finding β ij that minimizes the following loss function: (6) (7) where K x is an n x × n x kernel similarity matrix (K x) ij = k x(x i, x j), K y is an n y × n y kernel similarity matrix (K y) ij = k y y i, y j) and Z and B are matrices defined as (Z) ij = z ij and (B) ij = β ij(i = 1,2,···, n x, j = 1, 2,···, n y).

The conceptual domain of the matrix, defined as three core effects and their interaction with these five dimensions, provides a much-needed framework to underpin management of fragmented landscapes and highlights new research priorities.

with the matrix defined as (38).

where is the autocorrelation matrix defined as (B2).

where where is a selection matrix defined as (46).

Let denote the node distance matrix defined as.

here H is the covariance matrix defined as (3).

Let A be the matrix defined as in (2).

Let be an unitary Vandermonde matrix defined as in [13].