Standard Lemma guide

eigenvalue

noun · 2 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

Each Play button uses your device's default local English voice, or a natural local fallback. The selected voice name appears after playback. This is synthesized speech, not a source recording.

  • Received-Pronunciation: /ˈaɪ.ɡənˌvæl.juː/
  • General-American: /ˈaɪ.ɡənˌvæl.ju/
  • US: Recorded audio is listed in the source snapshot.
  • CMU ARPABET: AY1 G AH0 N V AE2 L Y UW0 Digits mark lexical stress: 1 primary, 2 secondary, 0 unstressed.

1

noun

Meaning 1

A scalar λ, such that there exists a non-zero vector x (a corresponding eigenvector) for which the image of x under a given linear transformation A is equal to the image of x under multiplication by λ; i.e. Ax=λx.

Definition source: English Wiktionary via Wiktextract

Topics: linear-algebra, mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: characteristic root, characteristic value, eigenroot, latent value, proper value

Antonyms: none provided

2

noun

Meaning 2

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

Definition source: Princeton WordNet 3.0

No example sentence was provided for this meaning.

Meaning relationships

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

Antonyms: none provided

Broader terms: value

History

Etymology

From eigen- + value. Partial calque of German Eigenwert.

Across languages

Translations

38 source translations are retained for this English entry.

  • Asturian: valor propiu — scalar multiplier of an eigenvector
  • Asturian: autovalor — scalar multiplier of an eigenvector
  • Catalan: valor propi — scalar multiplier of an eigenvector
  • Chinese Mandarin: 特徵值 /特征值 (tèzhēngzhí) — scalar multiplier of an eigenvector
  • Chinese Mandarin: 本徵值 /本征值 (běnzhēngzhí) — scalar multiplier of an eigenvector
  • Czech: vlastní hodnota — scalar multiplier of an eigenvector
  • Danish: egenværdi — scalar multiplier of an eigenvector
  • Dutch: eigenwaarde — scalar multiplier of an eigenvector
  • Estonian: omaväärtus — scalar multiplier of an eigenvector
  • Finnish: ominaisarvo — scalar multiplier of an eigenvector
  • French: valeur propre — scalar multiplier of an eigenvector
  • Galician: valor propio — scalar multiplier of an eigenvector
  • Galician: autovalor — scalar multiplier of an eigenvector
  • Galician: eigenvalor — scalar multiplier of an eigenvector
  • German: Eigenwert — scalar multiplier of an eigenvector
  • Greek: ιδιοτιμή (idiotimí) — scalar multiplier of an eigenvector
  • Hebrew: עֵרֶךְ עַצְמִי — scalar multiplier of an eigenvector
  • Hindi: अभिलाक्षणिक मान (abhilākṣaṇik mān) — scalar multiplier of an eigenvector
  • Icelandic: eigingildi — scalar multiplier of an eigenvector
  • Italian: autovalore — scalar multiplier of an eigenvector
  • Japanese: 固有値 (koyūchi) — scalar multiplier of an eigenvector
  • Lithuanian: tikrinė reikšmė — scalar multiplier of an eigenvector
  • Norwegian Bokmål: egenverdi — scalar multiplier of an eigenvector
  • Norwegian Nynorsk: eigenverdi — scalar multiplier of an eigenvector
  • Persian: مقدار ویژه (meqdâr-e viže) — scalar multiplier of an eigenvector
  • Polish: wartość własna — scalar multiplier of an eigenvector
  • Portuguese: autovalor — scalar multiplier of an eigenvector
  • Portuguese: valor próprio — scalar multiplier of an eigenvector
  • Portuguese: valor característico — scalar multiplier of an eigenvector
  • Romanian: valoare proprie — scalar multiplier of an eigenvector
  • Russian: со́бственное значе́ние (sóbstvennoje značénije) — scalar multiplier of an eigenvector
  • Slovak: vlastná hodnota — scalar multiplier of an eigenvector
  • Spanish: autovalor — scalar multiplier of an eigenvector
  • Spanish: valor propio — scalar multiplier of an eigenvector
  • Spanish: valor característico — scalar multiplier of an eigenvector
  • Spanish: eigenvalor — scalar multiplier of an eigenvector
  • Swedish: egenvärde — scalar multiplier of an eigenvector
  • Welsh: gwerth eigen — scalar multiplier of an eigenvector
Real reading context

eigenvalue in complete knowledge articles

Spectrum (functional analysis) Ideas & learning · Challenging · 9 uses Expander graph Ideas & learning · Challenging · 6 uses Rayleigh's quotient in vibrations analysis Technology & inventions · Advanced · 4 uses Weak formulation Ideas & learning · Challenging · 2 uses