Sentence examples for by the row matrix from inspiring English sources

More precisely, it is proved that if T has bounded characteristic function, then it is jointly similar to a contractive sequence of operators, i.e., there exists a similarity S∈B(H) such that the operator defined by the row matrix [ST1S−1 ST2S−1…STdS−1] is a contraction.

Proof Let μ k = λ k, ω k = -λ2m+2 - k, p k = 2, k = 1,..., m, ωm+1= s, pm+1= 1, then all the conditions of Theorem 3 are satisfied and Λ is realizable by the row stochastic matrix M defined in (9) by Theorem 3. In the case of Theorem 4, the matrix in (9) becomes the matrix in (13).

Therefore, Λ is realizable by the row stochastic matrix M in (13).

Examples for relevant outputs are the probability that the molecular copy numbers are in a certain domain Ω ¯ ⊂ Ω, which is achieved by the row vector output matrix C defined by C i = 1 if x (i ) ∈ Ω ¯, otherwise C i = 0, with p = 1, or the expected molecular copy numbers, given by (13) y e (t ) = ∑ i = 1 d x (i ) P i (t ), i.e. C = (x(1),…, x(d )) with p = n.

They are based on the property that the lumping schemes validated in the whole composition Yn-space of y are only determined by the invariance of the subspace spanned by the row vectors of lumping matrix M with respect to the transpose of the Jacobian matrix JT y) for the kinetic equations.

Likely, the most widely used random lattice with a lot of applications is of the knapsack type and defined by the row vectors of the following matrix (see also [4, 7, 29]): a 1 1 0 … 0 a 2 0 1 … 0 ⋮ ⋮ ⋮ ⋱ ⋮ a m 0 0 0 17 (17).

Under these power constraints, the corresponding scaling parameters αs 1, αs 2 and α r can be derived, where the average power of symbol A1u, A2u and B u are determined by the row weight of corresponding sampling matrix and sparsity probability of u.

Darker dots indicate a higher number of selective combinations containing the two nodes given by the row and column of the matrix.

We build a vector (row matrix) from the obtained matrix U1Σ11/2 by concatenating all rows, from 1 to 400, of matrix U1Σ11/2.

where,,, and, respectively, denote all zero entry, the matrix represented by the rows from until of, the matrix represented by the last rows of, and the matrix represented by the first rows of.

This matrix was formed by the row and column of the six blocks corresponding to the outputs and activities in each PDM, respectively.