ei·gen·val·ue

(ī′gən-văl′yo͞o)

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.]

American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

eigenvalue

(ˈaɪɡənˌvæljuː)

(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

Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

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

eigenvalue - (mathematics) any number such that a given square matrix minus that number times the identity matrix has a zero determinant

characteristic root of a square matrix, eigenvalue of a matrix, eigenvalue of a square matrix

value - a numerical quantity measured or assigned or computed; "the value assigned was 16 milliseconds"

Translations

egenværdi

Eigenwert

ιδιοτιμή

omaväärtus

ominaisarvo

eigingildi

autovalore

eigenwaarde

wartość własna

egenvärde

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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.

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