Sentence examples for exist matrix from inspiring English sources

In the following example we show that there exist matrix operators in the class (B overline{Delta{l_{1}}},l_{p})) which are not compact ((1leq{p}<infty)), that is, the limit in (20) may not be zero.

Finally, we end this section with the following example, which shows that the limit in (3.12) may not be zero, that is, there exist matrix operators in the class (mathcal{B}(bar{ell}_{1},{ell}_{p})) which are not compact, where (1leq p<infty).

If for prescribed scalars μ 1 > 0 and μ 2 > 1 satisfying ln ( μ 2 ) − β μ 1 < 0, there exist matrix X > 0, K ¯ and scalars ε 1 > 0, ε 2 > 0 such that the following linear matrix inequalities hold: [ μ 1 X + A X + X A T + B 1 K ¯ + K ¯ T B 1 T + ε 1 D 1 D 1 T K ¯ T N b T + X N T N b K ¯ + N X − ε 1 I ] < 0, (3.15).

Proof Suppose that there exist matrices Q ¯ 1 > 0 and Q ¯ 2 > 0, V and K ¯ satisfying (31) and (32).

Therefore, it can be concluded that if (16) holds, there must exist matrices Q 1 > 0, Q 2 > 0, V 1 and V 2 satisfying (12) and (13).

However, there exist matrices M E ∈ ℳ ( 2 ) having rank r M E < 3. We can now define a metric that depends on { T ( u r ) }.

(Sufficiency) When (22 - 24 22 - 24isfied, we firsatisfiedhat there exist matrices X, Y, Φ and Ψ such that (Y^{ - 1} - X) is nonsingular.

Consequently, the system with control of the form (18), (19) is absolutely stable if there exist matrices C 1, C 2 in (20) such that conditions (21 - 23 21 - 23lid.

Given a logarithmic quantizer as in (2), the closed-loop system in (8) is mean-square poly-quadratically stable if there exist matrices Q i > 0, X i > 0, V ¯ i and K satisfying (36) (36) (36).

By Theorem 5.4, H 1 is a J-SSE of H 0 if and only if there exist matrices M, N ∈ C 2 × 2 such that (5.6) and (5.7) hold.

Given a logarithmic quantizer as in (2), the closed-loop system (6) is mean-square poly-quadratically stabilized if there exist matrices Q ¯ 1 > 0, Q ¯ 2 > 0, V and K satisfying (31).