Sentence examples for matrices are understood from inspiring English sources

If B 1 and B 2 are normed spaces, then an operator g : B 1 → B 2 (nonlinear, in general) is positive homogeneous if g ( λ x ) = λ g ( x ) for every λ ∈ R + and x ∈ B 1. The inequalities between the matrices are understood componentwise.

The proposed algorithm is designed based on matrix-value operator learning techniques where the image patches are understood as the matrices and the single-image super-resolution is treated as a problem of learning a matrix-value operator.

For numerical convenience, we use a basis that is orthonormal, meaning the covariants satisfy (9) Tr (T i ⋅ T j ) = δ i, j, which also defines a generalized scalar product on the space of 4 × 4 matrices (any occurring Lorentz indices are understood to be summed over here).

In addition the glycoproteins such as cartilage oligomeric matrix protein (COMP) and tenascin-C are understood to be involved in collagen fibrillogenesis [ 20- 22].

The assumption on the connectivity of the product of Peron matrices can be understood intuitively as there being a uniform upper bound on the number of iterations required before information from one agent can propagate through the network to any other agent.

Because the random walk on the integrated network considers both types of interactions, each element P (i, j) of the corresponding transition matrix can be understood as the probability that proteins i and j have similar functions as these proteins are more likely to reach each other with a larger P (i, j).

Each column of matrix B can be understood as a sensitivity vector regarding each parameter.

Inequalities between real matrices or vectors will be understood componentwise, i.e., for two real l × q -matrices A = ( a i j ) and B = ( b i j ), the inequality A ≥ B means a i j ≥ b i j for i = 1, …, l ; j = 1, …, q.

In fact 12.5(the last equality arises from the fact that ρFb,Fb – ρIb,Ib = ρFa,Fa – ρIa,Ia according to eq 12.1); hence 12.6 In the classical rate picture arising from the assumption of zero off-diagonal density matrix elements, eq 12.6 is understood to arise from the fact that the EPT and ETa/PT2 or PT1/ETb reactions illustrated in Figure 20 correspond to the same initial and final states.

Oxidation kinetics of ceramic matrix composites dispersed with metallic particles is understood from the viewpoint of the diffusion properties and defect chemistry of matrix oxides.

The effects of this on the choice of pilots, the resulting precoder matrices and capacity performance need to be understood.