# eigenmatrix

## eigenmatrix

[′ī·gən‚mā·triks]
(mathematics)
Corresponding to a diagonalizable matrix or linear transformation, this is the matrix all of whose entries are 0 save those on the principal diagonal where appear the eigenvalues.
References in periodicals archive ?
In the situation of forced vibration, that is, [Q.sub.B] [not equal to] 0, there is a standard decoupling procedure for (A.2) by applying an eigenmatrix [X.sup.H] = [[X.sup.A.sub.H], [X.sup.B.sub.H]] which is composed of the series of A's eigenvectors, where the detailed definitions of [X.sub.A] and [X.sub.B] have been mentioned previously in Section 2.2 after (19) and (20), and note that Hermitian transposition of matrices has been employed here in consideration of the introduction of damping loss factors.
By assuming homogeneous boundary conditions, we have the nonlinear eigenmatrix problem
The eigenmatrix equation of the present approach can give nonphysical modes in addition to physical modes.
In the BBGFL, the eigenmatrix equations and the resonant wavenumbers are real.
The analytical solution for the natural frequency of the system can also be obtained using a basic eigenmatrix. Suppose that {[Z.sub.Z], [[theta].sub.X], [[theta].sub.Y], [[theta].sub.Z]} = {[[bar.Z].sub.Z][e.sup.[lambda]t], [[bar.[theta]].sub.X][e.sup.[lambda]t], [[bar.[theta]].sub.Y][e.sup.[lambda]t], [[bar.[theta]].sub.Z][e.sup.[lambda]t]}, which when substituted into the equation of motion for the rigid plate without a vibration absorber results in the following eigenmatrix:
Substituting [[bar.g].sup.*.sub.Na] into the original equation, we get the equilibrium [V.sup.*], and then substituting both [[bar.g].sup.*.sub.Na] and [V.sup.*] into eigenmatrix of (4), we can gain the eigenvalues as follows:
Then the points are substituted into eigenmatrix of (4) and the eigenvalues of the model can be calculated.
leads to single eigenvalues [lambda], the transformation matrix assumes the form S = [W.sup.-1], where W is an eigenmatrix obtained by solving eigenproblem (20), and matrix J = {[lambda]} = diag[[[lambda].sub.1], [[lambda].sub.2], [[lambda].sub.n]] becomes a diagonal matrix.
where [bar.C] is a 4 x 4 matrix called as eigenmatrix, [V.sup.t] = [[[E.sub.s][H.sub.s]].sup.t] = [[[E.sub.x][E.sub.y][H.sub.x][H.sub.y]].sup.t] (the superscript t denotes transpose of a matrix) is the state vector describing the state of the system.
For the entire EM problem space depicted in Figure 1, [bar.[mu]] is reduced to [[mu].sub.0]I ([[mu].sub.0] is the permeability in vacuum), and we have [k.sub.s] = 0 due to the normal incidence of the plane wave, so the eigenmatrix [bar.C] for any one region can be simplified greatly.
As for Region A and Region C, [bar.[epsilon]] is also reduced to [[epsilon].sub.0]I, and the eigenmatrix [bar.C] of these spaces will be more simple, which can be inferred from (11) through replacing [bar.[epsilon]] by [[epsilon].sub.0]I.
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