# eigenvalue equation

## eigenvalue equation

[′ī·gən‚val·yü i‚kwā·zhən]
(mathematics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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We write the generalized eigenvalue equation in the form of a standard eigenvalue equation as
From (7), (8), and (4), if the system has friction involved, then the complex eigenvalue equation is attained as follows:
Let us now look at the stationary eigenvalue equation, where we recall that n = 2m,
In Section 2 we present the model, compute equilibria, and derive the nth order eigenvalue equation which we need in order to perform stability and bifurcation analysis.
Constructing the Jacobian matrix from (5) and evaluating it at the two equilibrium points, we obtain the eigenvalue equation
It is obvious that [[mu].sub.1] = 0 is the first eigenvalue and [[mu].sub.2] = [[pi].sup.2] is the second eigenvalue of the eigenvalue equation
For the upper component (i = 1), we write the potential parameter as [m.sub.1] = [V.sub.0] + [S.sub.0] which gives the following energy eigenvalue equation from (14) as
Next applying the Method of Moments gives a linear eigenvalue equation that gives all the multi-band solutions simultaneously for a point in the first Brillouin zone.
The eigenvalue equation of the equilibrium point is locally asymptotically stable.

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