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Meaning of "eigenvalue" in the English dictionary

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DICTIONARY
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PRONUNCIATION OF EIGENVALUE

eigenvalue  [ˈaɪɡənˌvæljuː] play
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GRAMMATICAL CATEGORY OF EIGENVALUE

noun
adjective
verb
adverb
pronoun
preposition
conjunction
determiner
exclamation
Eigenvalue is a noun.
A noun is a type of word the meaning of which determines reality. Nouns provide the names for all things: people, objects, sensations, feelings, etc.

WHAT DOES EIGENVALUE MEAN IN ENGLISH?

Eigenvalues and eigenvectors

An eigenvector of a square matrix is a non-zero vector that, when the matrix multiplies, yields a constant multiple of, the latter multiplier being commonly denoted by. That is: The number is called the eigenvalue of corresponding to. If 2D space is visualized as a piece of cloth being stretched by the matrix, the eigenvectors would make up the line along the direction the cloth is stretched in and the line of cloth at the center of the stretching, whose direction isn't changed by the stretching either. The eigenvalues for the first line would give the scale to which the cloth is stretched, and for the second line the scale to which it's tightened. A reflection may be viewed as stretching a line to scale -1 while shrinking the axis of reflection to scale 1. For 3D rotations, the eigenvectors form the axis of rotation, and since the scale of the axis is unchanged by the rotation, their eigenvalues are all 1. In analytic geometry, for example, a three-coordinate vector may be seen as an arrow in three-dimensional space starting at the origin.

Definition of eigenvalue in the English dictionary

The definition of eigenvalue in the dictionary is 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.

WORDS THAT RHYME WITH EIGENVALUE


CDW
ˌsiːdiːˈdʌb əljuː
curlew
ˈkɜːljuː
devalue
diːˈvæljuː
disvalue
dɪsˈvæljuː
lew
ljuː
lieu
ljuː
misvalue
ˌmɪsˈvæljuː
MSW
ˌɛmɛsˈdʌbljuː
outvalue
ˌaʊtˈvæljuː
overvalue
ˌəʊvəˈvæljuː
purlieu
ˈpɜːljuː
revalue
riːˈvæljuː
transvalue
trænzˈvæljuː
UAW
ˌjuːeɪˈdʌbəljuː
UCW
ˌjuːsiːˈdʌbljuː
UMW
ˌjuːemˈdʌbəljuː
undervalue
ˌʌndəˈvæljuː
upvalue
ʌpˈvæljuː
UPW
ˌjuːpiːˈdʌbljuː
value
ˈvæljuː

WORDS THAT BEGIN LIKE EIGENVALUE

eigenfrequencies
eigenfrequency
eigenfunction
eigenmode
eigentone
eigenvector
Eiger
eight
eight ball
eight o´clock
eighteen
eighteenmo
eighteenth
eighteenthly
eightfoil
eightfold
eightfoot
eighth
eighth note
eighth-grader

WORDS THAT END LIKE EIGENVALUE

absolute value
acid value
added value
asset value
book value
calorific value
expected value
face value
food value
market value
net asset value
nominal value
par value
present value
Q value
replacement value
resale value
salue
store of value
surrender value
time value

Synonyms and antonyms of eigenvalue in the English dictionary of synonyms

SYNONYMS

Translation of «eigenvalue» into 25 languages

TRANSLATOR
online translator

TRANSLATION OF EIGENVALUE

Find out the translation of eigenvalue to 25 languages with our English multilingual translator.
The translations of eigenvalue from English to other languages presented in this section have been obtained through automatic statistical translation; where the essential translation unit is the word «eigenvalue» in English.

Translator English - Chinese

特征值
1,325 millions of speakers

Translator English - Spanish

valor propio
570 millions of speakers

English

eigenvalue
510 millions of speakers

Translator English - Hindi

eigenvalue
380 millions of speakers
ar

Translator English - Arabic

القيمة الذاتية
280 millions of speakers

Translator English - Russian

собственное
278 millions of speakers

Translator English - Portuguese

autovalor
270 millions of speakers

Translator English - Bengali

eigenvalue
260 millions of speakers

Translator English - French

valeur propre
220 millions of speakers

Translator English - Malay

Nilai eigen
190 millions of speakers

Translator English - German

Eigenwert
180 millions of speakers

Translator English - Japanese

固有値
130 millions of speakers

Translator English - Korean

고유
85 millions of speakers

Translator English - Javanese

Eigenvalue
85 millions of speakers
vi

Translator English - Vietnamese

eigenvalue
80 millions of speakers

Translator English - Tamil

eigenvalue
75 millions of speakers

Translator English - Marathi

Eigenvalue
75 millions of speakers

Translator English - Turkish

özdeğer
70 millions of speakers

Translator English - Italian

autovalore
65 millions of speakers

Translator English - Polish

wartość własna
50 millions of speakers

Translator English - Ukrainian

власне
40 millions of speakers

Translator English - Romanian

valoare proprie
30 millions of speakers
el

Translator English - Greek

ιδιοτιμή
15 millions of speakers
af

Translator English - Afrikaans

eiewaarde
14 millions of speakers
sv

Translator English - Swedish

egenvärdes
10 millions of speakers
no

Translator English - Norwegian

egenverdi
5 millions of speakers

Trends of use of eigenvalue

TRENDS

TENDENCIES OF USE OF THE TERM «EIGENVALUE»

The term «eigenvalue» is quite widely used and occupies the 45.817 position in our list of most widely used terms in the English dictionary.
0
100%
FREQUENCY
Quite widely used
79
/100
The map shown above gives the frequency of use of the term «eigenvalue» in the different countries.
Principal search tendencies and common uses of eigenvalue
List of principal searches undertaken by users to access our English online dictionary and most widely used expressions with the word «eigenvalue».

FREQUENCY OF USE OF THE TERM «EIGENVALUE» OVER TIME

The graph expresses the annual evolution of the frequency of use of the word «eigenvalue» during the past 500 years. Its implementation is based on analysing how often the term «eigenvalue» appears in digitalised printed sources in English between the year 1500 and the present day.

Examples of use in the English literature, quotes and news about eigenvalue

EXAMPLES

10 ENGLISH BOOKS RELATING TO «EIGENVALUE»

Discover the use of eigenvalue in the following bibliographical selection. Books relating to eigenvalue and brief extracts from same to provide context of its use in English literature.
1
The Symmetric Eigenvalue Problem
Mathematics of Computing -- Numerical Analysis.
Beresford N. Parlett, 1998
2
The Algebraic Eigenvalue Problem
A new paperback edition of Wilkinson's classic, pioneering text on the computation of matrix eigenvalues. One of the most important and widely-read books on numerical analysis ever published.
James Hardy Wilkinson, 1988
3
Variational Methods for Eigenvalue Problems: An Introduction ...
Purely mathematical treatment offers simple exposition of general theory of variational methods with special reference to the vibrating plate. No math beyond basic calculus. Includes exercises. 1957 edition.
Sydney Henry Gould, 1995
4
ARPACK Users' Guide: Solution of Large-scale Eigenvalue ...
This book is a guide to understanding and using the software package ARPACK to solve large algebraic eigenvalue problems.
Richard B. Lehoucq, Danny C. Sorensen, Chao Yang, 1998
5
Boundary and Eigenvalue Problems in Mathematical Physics
is, that it satisfies (VII.4), and we have seen in the preceding subsection that the eigenvalue corresponding to y(x) represents the minimum value of (VII. 5). As we have seen in Chapter V, §2, equation (VI 1. 4) has infinitely many solutions ...
Hans Sagan, 2012
6
The Matrix Eigenvalue Problem: GR and Krylov Subspace Methods
An in-depth, theoretical discussion of the two most important classes of algorithms for solving matrix eigenvalue problems.
David S. Watkins, 2007
7
Templates for the Solution of Algebraic Eigenvalue Problems: ...
Mathematics of Computing -- Numerical Analysis.
Zhaojun Bai, James Demmel, Jack Dongarra, 2000
8
Numerical Methods for Large Eigenvalue Problems: Revised Edition
This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices.
Yousef Saad, 2011
9
Numerical Methods for General and Structured Eigenvalue Problems
This book is about computing eigenvalues, eigenvectors and invariant subspaces of matrices.
Daniel Kressner, 2006
10
Spectral Generalizations of Line Graphs: On Graphs with ...
This book deals with all these families of graphs in the context of their spectral properties. The authors discuss the three principal techniques that have been employed, namely 'forbidden subgraphs', 'root systems' and 'star complements'.
Dragoš Cvetkovic, Peter Rowlinson, Slobodan Simic, 2004

10 NEWS ITEMS WHICH INCLUDE THE TERM «EIGENVALUE»

Find out what the national and international press are talking about and how the term eigenvalue is used in the context of the following news items.
1
Psychometric properties of a brief measure of autonomy support in …
For overall treatment experience and provider specific scales, only one Eigenvalue was greater than 1.0, and in each case the percentage of ... «BMC Blogs Network, Jul 15»
2
Supplementary Data
... Principal Component 1 (which explained 70.5% of the variation from the principal component analysis and had an eigenvalue of 2.8) used as ... «Am J Botany, Jun 15»
3
Fiber guiding at the Dirac frequency beyond photonic bandgaps
... single frequency and should be distinguished from a recent observation of an 'embedded eigenvalue' that also occurs at a single frequency. «Nature.com, Jun 15»
4
Complete temporal characterization of a single photon
The primary eigenvector of the TDM has a corresponding eigenvalue almost 45 times larger than the second largest one indicating a nearly ... «Nature.com, Jun 15»
5
Quantum Discord for d⊗2 Systems
where stands for the largest eigenvalue of the matrix . Eq. (7) gives the analytical formula for the classical correlation in terms of linear entropy ... «Nature.com, Jun 15»
6
Sparking New Ideas In Econometrics
This is because the largest eigenvalue cannot be accurately estimated if the cross-sectional dimension grows at the same rate as the sample ... «Asian Scientist Magazine, May 15»
7
Tipping points and early warning signals in the genomic …
For this reason, its largest eigenvalue is positive, it verifies that λ1 > |λi|, ∀ i > 1, and the elements of its associated eigenvector are also positive ... «Nature.com, May 15»
8
It's complicated: Self-organized patterns identify emergent behavior …
The final obstacle was mathematically proving that the first eigenvalue (each of a set of values of a parameter for which a differential equation ... «Phys.Org, Apr 15»
9
Depressive symptoms and clustering of risk behaviours among …
The following criteria were used to determine the number of clusters: factors must have an eigenvalue of >1.00 and factor loadings must have ... «BMC Blogs Network, Apr 15»
10
Conservatism and novelty in the genetic architecture of adaptation in …
This analysis was extended by performing multivariate analysis on all principal components with an eigenvalue greater than or equal to ... «Nature.com, Mar 15»

REFERENCE
« EDUCALINGO. Eigenvalue [online]. Available <https://educalingo.com/en/dic-en/eigenvalue>. Apr 2024 ».
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