Sentence examples for matrix we know from inspiring English sources

Based on the transportation mode/disaster-phase combination matrix, we know that most articles addressed the response phase, and the preparedness/response phase combination coming second.

Proof of Theorem 3 From x i > 0 ( i = 1, 2, …, n + 1 ) and the edge matrix M = ( cos ρ i j ) i, j = 1 n + 1 of  Ω n being a positive definite symmetric matrix, we know that the matrix Q in (15) is also a positive definite symmetric matrix.

By Lemma 2.5, we have a i i = ∑ j ≠ i | a i j | + 1 = ∑ j ≠ i | a j i | + 1 and a i i > 1, i ∈ N. Denote u j = max i ≠ j { u j i } = max { | a j i | + ∑ k ≠ j, i | a j k | m k i a j j }, j ∈ N. Since A is an irreducible matrix, we know that 0 < u j ≤ 1.

Bullock huddles into herself, returning to fetal position, and the camera pans in and the lighting follows accordingly, so like Neo in the last Matrix we know for 1000% sure that he is the one, and that Bullock will be reborn.

Although it manifests itself histologically as an increase in extracellular matrix, we know that the histological appearance can be caused by a de novo synthesis of matrix (primarily collagen), or a disproportionate loss of renal parenchyma.

If A is an M-matrix, we know that there exists a diagonal matrix D with positive diagonal entries such that (D^{-1}AD) is a strictly row diagonally dominant M-matrix.

We also note that diag { ( 1 + sinh f i ( x ) μ 1 + cosh f i ( x ) μ ) : i ∈ N } and εI are positive diagonal matrices, we know that Φ x ′ ( z ) is nonsingular by Lemma 2.1, which implies that H ′ ( z ) is also nonsingular.

If the product Wi ra,c Wj rb,c) = 0, then from one or both of the matrices we know that the agent cannot be in state Si(c).

For SPD matrices we know that the eigenvalues can be estimated in terms of the Rayleigh quotients.

Furthermore, by using random matrix theory for the matrix Φ, we know that (mathbb {E} {|Phi |} le sqrt {n}+sqrt {m}) and (|Phi | le sqrt {n}+sqrt {m}+t) with probability at least (1-2 e^{-t^{2}/2}) for all t≥0 (see, e.g., [30]).

Also in this case, in terms of eigenvalues of the adjacency matrix A G, we know the distribution of poles of (tilde {mathbf {Z}}_{G} u)).