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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.]


(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


(ˈaɪ gənˌvæl yu)

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:
Noun1.eigenvalue - (mathematics) any number such that a given square matrix minus that number times the identity matrix has a zero determinant
value - a numerical quantity measured or assigned or computed; "the value assigned was 16 milliseconds"
wartość własna
References in periodicals archive ?
Eigenvalues are thereby ideal candidates for information transport.
Reanalysis methods estimate the eigenvalues and eigenvectors of a modified design without performing a full-order eigenvalue analysis.
When the real parts of complex eigenvalues are positive (negative damping) the complex eigenvalues and corresponding complex mode shapes or vectors are unstable and could result in unwanted brake noise.
The primal space, which forms the global, coarse part of the domain decomposition algorithm and which is always required for any competitive algorithm, is defined in terms of generalized eigenvalue problems related to subdomain edges and faces; selected eigenvectors associated to the smallest eigenvalues are used to enhance the primal spaces.
Since the seminal paper of von Neumann and Wigner [13], Schrodinger operators with embedded positive eigenvalues have always played a special role in spectral and in scattering theory.
The related idea, as far as we know, can be traced to the work of Poincare; he found that [3] if the Jacobian matrix A = Du(0) is diagonal and the eigenvalues [[lambda].
They are divided into linear and nonlinear problems of eigenvalues.
In [1], Adivar and Bohner investigated the eigenvalues and the spectral singularities of non-selfadjoint q-difference equations of second order with spectral singularities.
The zeros of (G, ) are eigenvalues of A and multiset of eigenvalues of A is called the spectrum of A .
The scree test is a heuristic graphic method that consists of: a) plotting the eigenvalues (y-axis) against the components (x-axis), and b) inspecting the shape of the resulting curve in order to detect the point at which the curve changes drastically (and the "scree on the hill slope" begins).
Eigenvalues In Riemannian Geometry, Academic Press, Inc.