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Related to eigenvalue: eigenvalue equation, Eigenvalue Problem


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 ?
The rule consists of retaining a given component if the associated eigenvalue is bigger than the mean (or a given percentile) of those obtained from the simulated samples (Ledesma & Valero-Mora, 2007).
The first non-nule eigenvalue v(M) of L is called the first eigenvalue of the Oteklon problem and it is variationaly characterized lay:
Part III covers numerical methods for linear systems and eigenvalue computation with a recent topics list.
For a real symmetric matrix M, the real number [lambda] is an eigenvalue of a matrix M if there exists a nonzero vector x (termed a [lambda]-eigenvector) satisfying Mx = [lambda]x.
If [lambda] is a complex eigenvalue of the matrix L, then [lambda] satisfies the discrete Euler-Lotka equation
Eigenvalue based spectrum sensing methods have been widely studied recently.
The appropriate number of factors to retain is achieved by making a one to one comparisons of the eigenvalues, keeping the empirical eigenvalue that is less than the random eigenvalue.
The progress of these TCs can be concluded mathematically from their eigenvalue distributions.
This can be generated using JMP Principal Components Analysis on Correlations (see Figure 5, eigenvalue = 0.
If G is regular of degree [delta], then these conditions are equivalent, since every eigenvector of A with eigenvalue [lambda] is an eigenvector of L with eigenvalue [delta] - [lambda].
The eigenvalue based spectrum sensing algorithm is provided in section 4.
In these cases, errors of eigenvalue sample estimations result in noticeable errors in the calculations of diversity gains and capacities.