Sentence examples for be a matrix exponential from inspiring English sources

Let be a matrix exponential function of (3.2).

Thus, is a matrix exponential function of (3.2).

where is a matrix exponential function of (3.2).

Let, where is a matrix exponential function of (3.17).

The formal solution to (18) can be constructed using variation of parameters as Q xi) = G xi,xi_{0}) Q xi_{0}) + int_{xi_{0}}^{xi}Gbigl xi,xi'bigr) widehat{Psi}bigl xi'bigr),mathrm {d}xi', (23) where G is a matrix exponential given by Gbigl xi,xi'bigr) = mathcal{T} biggl{ exp biggl( int_{xi'}^{xi} mathrm {d}s A(s) biggr) biggr}.

The number of 'virtual' events n v, which includes the 'do nothing' transitions, is distributed according to (5) P (n v | d i, d j ) = P (n v ) [ R n v ] d i, d j [ e m Δ ] d i, d j where Δ = t j − t i, P (n v ) is a Poissonian with rate parameter λ Δ, R is the stochastic matrix m / λ + I and e m Δ is a matrix exponential.

In fact, the symbol function (H xi )) is a matrix polynomial in complex exponential.

A multiscaling function is characterized by a unique symbol function, which is a matrix polynomial in complex exponential.

In our notation, the exponential term in Equation 9 is a matrix whose elements are made of the exponential values of the corresponding distance matrix elements.

In the time-stepping process of the proposed method, the column vector containing the spatially sampled field values is updated by multiplying it with an iteration matrix, which is written in a matrix-exponential form.

where T ⊂ R ≥ 0 is a time scale and A = ( 0 0 0 − 2 ) and investigated some types of stability of Eq. (7.1) when A is regressive, i.e., μ ( t ) ≠ 1 2 for all t ∈ T. In this case the equation has the unique solution x ( t ) = e A ( t, 0 ) x 0, where e A ( t, 0 ) is the matrix exponential function.