# Definitions for eigenvalueˈaɪ gənˌvæl yuei·gen·val·ue

### Princeton's WordNetRate this definition:0.0 / 0 votes

1. eigenvalue, eigenvalue of a matrix, eigenvalue of a square matrix, characteristic root of a square matrixnoun

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

### WiktionaryRate this definition:0.0 / 0 votes

1. eigenvaluenoun

The change in magnitude of a vector that does not change in direction under a given linear transformation; a scalar factor by which an eigenvector is multiplied under such a transformation.

The eigenvalues uE000117279uE001 of a transformation matrix uE000117280uE001 may be found by solving uE000117281uE001 .

### WikipediaRate this definition:0.0 / 0 votes

1. eigenvalue

In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by λ {\displaystyle \lambda } , is the factor by which the eigenvector is scaled. Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated.

### ChatGPTRate this definition:0.0 / 0 votes

1. eigenvalue

An eigenvalue is a scalar associated with a linear system of equations (i.e., a matrix), which characterizes the magnitude by which an associated vector, called an eigenvector, is scaled during a linear transformation represented by the matrix. In other words, if applying a matrix transformation to an eigenvector only changes the scale of the eigenvector, and not its direction, then the scale factor is the eigenvalue.

### Numerology

1. Chaldean Numerology

The numerical value of eigenvalue in Chaldean Numerology is: 4

2. Pythagorean Numerology

The numerical value of eigenvalue in Pythagorean Numerology is: 2

### Popularity rank by frequency of use

eigenvalue#10000#32933#100000

## Translations for eigenvalue

• ιδιοτιμή
• valor propio

### Translation

#### Find a translation for the eigenvalue definition in other languages:

Select another language:

• - Select -
• 简体中文 (Chinese - Simplified)
• Español (Spanish)
• Esperanto (Esperanto)
• 日本語 (Japanese)
• Português (Portuguese)
• Deutsch (German)
• العربية (Arabic)
• Français (French)
• Русский (Russian)
• 한국어 (Korean)
• עברית (Hebrew)
• Gaeilge (Irish)
• Українська (Ukrainian)
• اردو (Urdu)
• Magyar (Hungarian)
• मानक हिन्दी (Hindi)
• Indonesia (Indonesian)
• Italiano (Italian)
• தமிழ் (Tamil)
• Türkçe (Turkish)
• తెలుగు (Telugu)
• ภาษาไทย (Thai)
• Tiếng Việt (Vietnamese)
• Čeština (Czech)
• Polski (Polish)
• Bahasa Indonesia (Indonesian)
• Românește (Romanian)
• Nederlands (Dutch)
• Ελληνικά (Greek)
• Latinum (Latin)
• Svenska (Swedish)
• Dansk (Danish)
• Suomi (Finnish)
• فارسی (Persian)
• ייִדיש (Yiddish)
• հայերեն (Armenian)
• Norsk (Norwegian)
• English (English)

## Citation

#### Use the citation below to add this definition to your bibliography:

Style:MLAChicagoAPA

"eigenvalue." Definitions.net. STANDS4 LLC, 2024. Web. 15 Aug. 2024. <https://www.definitions.net/definition/eigenvalue>.

## Are we missing a good definition for eigenvalue? Don't keep it to yourself...

#### Free, no signup required:

Get instant definitions for any word that hits you anywhere on the web!

#### Free, no signup required:

Get instant definitions for any word that hits you anywhere on the web!

### Quiz

#### Are you a words master?

»
##### an onerous or difficult concern
A hypernym
B flair
C encumbrance
D serendipity