A comparison of the matrix formulation, complex Gaussian expansion and direct numerical integration of the Collins formula is made, where the propagation of apertured Laguerre鈥揋aussian beams is chosen as an illustrative example. It is shown that the matrix formulation provides satisfactory results in...
Intensity MatrixCharacteristic EquationsState ProbabilitiesTechnical system consisting of two independent subsystems (e.g. hybrid car) is considered. Graduated state graph being homogenous ergodic system of symmetric structure is constructed for the system. Differential Kolmogorov equations, describing homogenous...
In a new empty cell type = MMULT(matrix_N1, matrix_N) and then press enter key. Starting with the cell with MMult formula, highlight 3 by 3 cells. Press F2, and it will be appear like the following figure Then press CTRL-SHIFT-ENTER together you get the symmetric matrix as shown ...
The Hurwitz–Kontsevich model (58) is a matrix model [11] Z0{p}=∫N×Ndet(sinh(ϕ⊗I−I⊗ϕ2)ϕ⊗I−I⊗ϕ2)×dϕe−12tTrϕ2−N2Trϕ−16tN3+124tN+Tr(eϕψ), where ψ is an N×N matrix and the time variables pk=Trψk, which can be represented...
(2) In the computational process, each prediction requires solving the inverse matrix of a third-order matrix, which is less computationally intensive each time but can take much time, considering that this process will be heavily used in the search process. Therefore, this paper proposes a ...
Here is the demo, please try it: How to build a Dynamic Symmetric Matrix I’m not sure the formula, what do “LAPT1” and “LONP1” mean? If you need a calculated outcome, please details. Best Regards, Link Message 3 of 4 872 Views 0 Reply parry2k Super User 01-09-202...
(1.2) where, andis the standard simplectic matrix in, see Theorem 4.1 and Corollaries 4.2, 4.3 of [35]. The next important generalization was to consider system (1.2) with HamiltonianHfor whichis an isolated degenerate critical point of the HamiltonianHwith nontrivial Conley index i.e.,is...
When is a monic polynomial the characteristic polynomial of a symmetric matrix over a field? A theorem on determinants of matrices commuting with a given matrix provides a simple necessary condition. The condition is sufficient over local number fields except for certain irreducible quartic polynomials...
As examples of applications of the new formulae, spin-own-orbit and scalar spin—spin matrix elements were derived. 1997 John Wiley & Sons, Inc.doi:10.1002/(SICI)1097-461X(1997)61:13.3.CO;2-BN. FlockeM. BaryszJ. KarwowskiG. H. F. Diercksen...
On the symmetric solutions of a linear matrix equation A formula for the partitioned minimum-norm reflexive generalized inverse is applied to find the general symmetric solution X to the matrix equation AX=B. A... J F.,Henk,Don - 《Linear Algebra & Its Applications》...