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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 ?
First, [partial derivative]F/[partial derivative]U has real eigenvalues {a + bu, [0.
The eigenvalues are representations of the variance variables share.
it has only finite eigenvalues plus infinite eigenvalues with Kronecker blocks of size one due to the fact that [DELTA] and [[SIGMA].
Part I covers the basic concepts of linear algebra, including vectors and matrices, linear independence and basis sets, determinants, eigenvalues, product spaces, and orthogonality, canonical forms, matrices with special properties such as Hermitian and unitary, and spectral theory.
Wigner also discovered that the statistics of gaps can be modelled by eigenvalues of large random matrices.
The Leslie matrices, their eigenvalues and the predictions for each set of data were obtained by using the software MATHEMATICA 8.
In [1] and [2] the formulae for the determinant, eigenvalues, Euclidean norm, spectral norm and inverse of the right circulant matrices with arithmetic and geometric sequences were derived.
Diagnostic tests for collinearity are: VIF (variance inflation factor), correlation matrix of variables, eigenvalues and eigenvectors, condition indices, variance proportions.
1 For every n [greater than or equal to] 1, the simplicial rook graph SR(3, n) is integral and Laplacian integral, with eigenvalues as follows:
today announced the availability of an automated multilevel substructuring eigenvalue solver (AMSES) that dramatically cuts the time required to compute eigenvalues for analysis in noise, vibration and harshness (NVH) simulations.
Thus, the shape was taken from the first canonical variate axis showing the highest eigenvalue since the largest eigenvalues correspond to the dimensions that have the strongest correlation in the data set.