eigenvalue


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Related to eigenvalue: eigenvalue equation, Eigenvalue Problem

ei·gen·val·ue

(ī'gĕn-val-yū),
Any of the possible values for a parameter of an equation for which the solution will be compatible with the boundary conditions. Compare: eigenfunction.
[Ger. eigen, particular, peculiar to]
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all roots of the equation det(z[alpha](z)I - A) =0 are inside the unit circle if and only if all eigenvalues of A belong to {z[alpha](z) :[absolute value of z] < 1>.
We note that part of this work was presented at the 24th International Conference on Domain Decomposition Methods and at the same conference an adaptive FETI-DP algorithm with a change of basis formulation was presented by Axel Klawonn, where different generalized eigenvalue problems are introduced and different tools are used in the analysis of condition numbers.
The operator matrix, L, has real-valued eigenvalues that are always greater than or equal to 1.
It is the purpose of this paper to show the existence of the principal eigenvalues and determine the sign of the corresponding eigenfunctions for linear periodic eigenvalue problem
[E.sub.n] and [mu] = [m.sub.1][m.sub.2]/([m.sub.1] + [m.sub.2]) are energy eigenvalue of nth level and reduced mass of the q[bar.q] system, respectively ([m.sub.1] and [m.sub.2] are quark masses).
Kostic and Voss [9] applied the Sylvester's law of inertia on the definite quadratic eigenvalue problems.
If all the adjacent neighbour average sequences [z.sup.(1).sub.i](k) [greater than or equal to] 1 and the chosen sample is the minimal permitted data in grey system, then we conclude that [[summation].sup.n.sub.k=2][([z.sup.(1).sub.i](k)).sup.2] is larger than n - 1, and the maximal eigenvalue and minimal eigenvalue are contained in different circles, and the centres of circles are far from each other.
For the eigenvalue assignment in [A.sup.r.sub.z,2], we encounter singularly perturbed structure so that the two-stage design is applied to the slow and fast subsystems.
In this paper we consider the fractional extension of the Sturm-Liouville eigenvalue problem