Sentence examples for matrix as stated from inspiring English sources

Computation of structure's mass matrix as stated in Sect.

Moreover, when the K NFLs are chosen from ( {C}_2^{N-1} ) possible combinations, the objective function in (1) is also represented as a Laplacian matrix as stated in the following theorem.

Therefore, we changed the final computation step of the 4D FAP to perform an optimal assignment on the matrix S as stated in Equation 19.

Let m be the number of ones in the matrix M. As stated earlier, the number of biclusters in the input is n.

Any (mtimes n) matrix can be decomposed into a diagonal matrix of its singular values and orthogonal matrices of order m and n as stated in [16], Theorem 6.1, quoted below as.

Remark 2: As stated in Section 2-D, the covariance matrix is a two-level Hermitian Toeplitz matrix.

The final transformation matrix was used to transform each mask to standard space as stated above.

The advantage of this control scheme is that the input matrix as well as the output matrix of the state space realization of the discretized plant can be assigned arbitrarily by appropriate choice of hold and sampling functions.

As stated above, we have the translation and rotation matrices from the three receivers.

By extending the elements of the state covariance matrix as augmented states, the statistical behavior of the trajectory is captured to reformulate the performance metrics and path constraints.

Denote by λ 1 ≤ λ 2 ≤ ⋯ ≤ λ n the eigenvalues of an Hermitian matrix A. The matrix version of the well-known Kantorovich inequality for a positive definite matrix A is stated as follows (see, e.g., [1, 2]): 1 ≤ x ∗ A x x ∗ A − 1 x ( x ∗ x ) 2 ≤ ( λ 1 + λ n ) 2 4 λ 1 λ n (1.1).