eigenvalue

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Related to eigenvalue: eigenvalue equation, Eigenvalue Problem

ei·gen·val·ue

(ī′gən-văl′yo͞o)
n.
The factor by which the magnitude of an eigenvector is changed by a given transformation.

[Partial translation of German Eigenwert : eigen-, peculiar, characteristic (from eigen, own, from Middle High German, from Old High German eigan; see aik- in Indo-European roots) + Wert, value.]

eigenvalue

(ˈaɪɡənˌvæljuː)
n
(Mathematics) maths physics one of the particular values of a certain parameter for which a differential equation or matrix equation has an eigenfunction. In wave mechanics an eigenvalue is equivalent to the energy of a quantum state of a system

ei•gen•val•ue

(ˈaɪ gənˌvæl yu)

n.
a scalar for which there exists a nonzero vector such that the scalar times the vector equals the value of the vector under a given linear transformation.
[1925–30; < German Eigenwert,=eigen- characteristic, particular + Wert value]
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 eigenvalue - (mathematics) any number such that a given square matrix minus that number times the identity matrix has a zero determinantvalue - a numerical quantity measured or assigned or computed; "the value assigned was 16 milliseconds"
Translations
egenværdi
Eigenwert
omaväärtus
ominaisarvo
eigingildi
wartość własna
egenvärde
References in periodicals archive ?
Exploring recent results in spectral geometry and its links with shape optimization, contributors are interested with whether there exists a set that minimizes (or maximizes) the k-th eigenvalue of a given elliptic operator with given boundary conditions, among sets of given volume, and if so what can be said about the regularity of the optimal set.
Hence the eigenvalue [lambda] of the matrix A lies outside of the image of unit circle in the mapping [bar.[alpha]] : C [right arrow] C given by [bar.[alpha]](z) = z[alpha](z).
We note that for all such algorithms certain generalized eigenvalue problems are solved to select the set of adaptive primal constraints under a given tolerance value.
The asymptotic eigenvalue matrix [D.sup.[infinity]] is a diagonal matrix with eigenvalues [[lambda].sup.[infinity].sub.n] = 1 only at loci where matrix G is zeroed, and [[lambda].sup.[infinity].sub.n] = 0, where g[n] > 0.
Ifthe domain [OMEGA] is such that every eigenvalue of -[DELTA] + V is simple, then
In 1997, Constantin  studied the following linear periodic eigenvalue problem:
As a field of application, AIM can be used to deal with Schroodinger equation (or energy eigenvalue problem) in mathematical physics.
The purpose of this work is to (1) study the analytic behaviour of the eigenvalue E([lambda]) near the coupling constant threshold and (2) study the asymptotic behaviour of the discrete spectrum in the gaps of the spectrum of [H.sub.0] as the coupling constant grows to infinity.
In the engineering practice eigenvalue problem is very important because it is related with the mechanical systems and their property of vibration.
where [[lambda].sub.max] is the maximal eigenvalue of the matrix and [[lambda].sub.min] is the minimal eigenvalue of matrix.
In (11) and (14) we have chosen the feedback gains for the eigenvalue assignment problem.

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