Sentence examples for if matrices from inspiring English sources

If matrices almost satisfying a group relation are close to matrices exactly satisfying the relation, then we say that a group is matricially stable.

Even if matrices with finite dimensions are not free, the free probability framework, based on the moments, can still be used to propose an algorithmic method to compute these operations for finite size matrices.

In general case, if matrices ( a i, j k ) of operators ( A k + f ) j = ∑ j = 1 i a i, j k f j belong to the classes O m k +, k = 1, …, n, then the matrix of operator A n + ≡ A 1 + ∘ A 2 + ∘ ⋯ ∘ A n + belongs to the class O m +, where m = ∑ k = 1 n m k + n - 1.

Similarly, if matrices ( a i, j k ) of operators ( A k - g ) j = ∑ i = j ∞ a i, j k g i belong to the classes O m k -, k = 1,..., n, then based on Lemma 2.2, Theorem 3.2 gives necessary and sufficient conditions for boundedness and compactness of operator A n - = A 1 - ∘ A 2 - ∘ ⋯ ∘ A n - from l p,v into l q,u, 1 < p ≤ q < ∞.

Thus, steady-state vectors π (i ) are relatively close to each other if matrices Q and (Q + Δ Q) are close and ‖ Q#‖ is not large.

It is interesting to find that toughening is efficient only if matrix crystallinity and particle size are well matched.

If matrix factorization is performed, the contextual information at node (R_{22}) can not be taken advantage.

If matrix permeability is extremely low, gas well cannot achieve the industrial production even after fracturing.

However, if matrix order changes, the number of coefficients also will change in a factorial way.

If matrix A is singular then, the problem is infeasible and we are done.

Moreover, it is shown that ∥x t)∥R is monotonically decreasing for sufficiently large t if matrix A is asymptotically stable.