Sentence examples for matrix equation can from inspiring English sources

Matrix equation can be constructed as: (5).

This global matrix equation can be solved to determine the wave propagation coefficients.

Hence the resultant matrix equation can be solved and the unknown Taylor coefficients can be found approximately.

The resulting schemes in each ADI solution step corresponding to a strictly diagonally dominant matrix equation can be solved using the 1D tridiagonal Thomas algorithm with a considerable saving in computing time.

For each epoch, t i, Eq. (6) can be linearized as follows: (7) where the observation matrix g i and the state vector δx are defined by: (8) (9) For N-point kinematic solutions, the following matrix equation can be formulated: (10) Finally, the optimal state vector,, which minimizes the squared-sum of the residual vector, e T e, is obtained from: (11).

Given a metabolic network, a matrix equation can be used in order to describe the mass balances around the nodes, the m internal metabolites: (1) d c dt = S · v in which c is a vector of metabolite concentrations and v is the vector of reaction rates, or fluxes, representing the mass flow through each of the n reactions in the network [ 8].

Many problems in various areas, such as differential equations, integral equations, boundary value problems and nonlinear matrix equations, can be converted to the operator equation (1.1).

When a special kind of initial iteration matrix group is chosen, the unique least-norm generalized reflexive solution of the general coupled matrix equations can be derived.

The least Frobenius norm generalized reflexive solution of the general coupled matrix equations can be derived when an appropriate initial matrix group is chosen.

Any number of such matrix equations can always be rewritten as a system of equations whose most general form reads where P has 6 columns and 6 n rows, where n is the number of symmetry elements other than the identity involved in the special position [indeed equation (10), being trivial for, can safely be discarded].

As a special case of Example 3.1, one can consider the following matrix equation, which can also be found in [19]: X-A_{1}^{ast}XA_{1}-cdots-A_{m}^{ast}XA_{m}=Q, where Q is a positive definite matrix and (A_{1},ldots, A_{m}) are arbitrary (ntimes n) matrices with (sum_{n=1}^{m}|A_{n}|<1) with (pgeq1).