Sentence examples for matrix we obtained from inspiring English sources

Applying the fundamental solution matrix of coefficient matrix, we obtained a series of new sufficient conditions to guarantee the existence and global exponential stability of an anti-periodic solution for the BAM neural networks with time-varying delays in the leakage terms.

From each matrix, we obtained 10 parameters commonly used to describe network structure.

Using information of the eigenvalues of the adjacency matrix, we obtain necessary conditions for existence.

Considering the unitarity of WFRFT matrix, we obtain (E|mathbf {d}_{alpha }|_{2}^{2}=E|mathbf {d}|_{2}^{2}).

From this matrix we obtain the magnetic energy distribution in the wave vector domain.

Taking conjugation (Q^{-1} (cdot) Q) by the matrix we obtain the second part of our assertion.

Therefore, there exists a positive constant such that and from the properties of matrix, we obtain (4.11).

Together with the local phase matrix, we obtain a certain wave transmitting from a layer to the neighboring one.

Applying the item (b) of Proposition 3 to this matrix we obtain ρ ( A + B Δ ) = ρ ( A ˆ + B ˆ Δ ˆ ) < 1 if and only if δ < | I − A | b.

By properties on the strictly diagonally dominant matrix and the normal matrix, we obtain rho(T leq|T|_{2}leq frac{1}{2} bigl[ rho I-gamma G_{1})+rho I-gammaa G_{2}) bigr]< 1} (28) where (rho(T)), (rho(I-gamma G_{1})) and (rho(I-gamma G_{2})) are the spectral radii of the matrices T, ((I-gamma G_{1})) and ((I-gamma G_{2})).

After redefining the ordering matrix, we obtain a sequence of transition matrices T q corresponding to Y q = { ( y q 2 i − 1 ) : ( y i ) ∈ Y } for q = 2 k + 1, k ≥ 0. The following theorem exhibits the computation of Γ n ( Y ) and h ( Y ).