eigenvalue

/ˈaɪ.ɡənˌvæl.juː/

//ˈaɪ.ɡənˌvæl.juː// noun

By · According to Wiktionary data (CC BY-SA) ·

"eigenvalue" is a 10-letter English headword indexed on PlainSpell.

The verdict

“eigenvalue” is uncommon English (frequency #60,786 among 2,246 “E” headwords), classed as a noun. The kind of spelling people second-guess.

#60,786
frequency rank, English
2,246
“E” headwords

According to Wiktionary data (CC BY-SA, analyzed September 3, 2026) - 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 b...

Corpus desk

Index EN-eigenvalue · eigenvalue · English

eigenvalue · rank #60,786 · 0 variants · 0 confusables

  • FREQ-RARE #60,786
  • LEN-MEGA 10 letters
  • VOW-6 6 vowels
  • CONFUS-0 No pairs
  • VAR-0 0 variants
  • BOOK-MID 2,246
  • PHOTO-FINISH egoism

Nearest frequency peer: egoism (-1 rank slots)

Read with this headword: Spelling guide for this pattern

Desk codes from Wiktionary headword shape, FrequencyWords rank tier, confusable-pair count, generated misspelling depth, letter-cohort book size, and photo-finish peer. Not a difficulty grade.

Long-tail ranks near “eigenvalue”

Sparse band: bars invert rank so rarer forms read shorter

corpus weight

What this shows Long-tail view: where “eigenvalue” sits against similarly uncommon English ranks.

Source FrequencyWords open word-frequency list As of September 3, 2026
Key facts for eigenvalue
PropertyValue
Headwordeigenvalue
LanguageEnglish
Part of speechNoun
IPA/ˈaɪ.ɡənˌvæl.juː/
Letters10
Frequency rank#60,786
Misspellings tracked0
Confusable pairs0
SourceWiktionary (kaikki.org)

Long-tail rank of “eigenvalue” in English

Word frequency stretches from the small set of words we reach for constantly (left) out to the long tail barely used once in a while (right).eigenvaluefalls in this rarity band:

#1#100#1K#10K#100K
← used constantlyrarely used →

Ticks step logarithmically, so each one marks a roughly tenfold drop in how often the word turns up. Rare peers in the same band: “egoism” (#60,785), “eir” (#60,787), “educative” (#60,784). Among 2,246 “E” headwords, “eigenvalue” is #60,786. Source: FrequencyWords open word-frequency list.

Rare enough to double-check

eigenvalue is uncommon English at frequency #60,786 among 2,246 “E” headwords, classed as anoun, transcribed /ˈaɪ.ɡənˌvæl.juː/. Rarity is why readers land here mid-draft. Gloss: "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 b...".

No misspelling variants are generated for eigenvalue in our index, a sign its spelling follows regular English conventions. Our dataset records no confusable match here, a sign it's visually distinctive enough not to be mixed up with another word.

Etymologically, the entry records: From eigen- + value. Partial calque of German Eigenwert. The correct English form is eigenvalue, spelled E-I-G-E-N-V-A-L-U-E.

Definition

  1. 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.

Recorded use

Wiktionary examples

These source excerpts show how eigenvalue appears in context. They illustrate usage; the definition above remains the entry’s reference meaning.

  1. In the extension, one associates eigenvalues, sets of scalars, with arrays of matrices by considering the singularity of linear combinations of the matrices in the various rows, involving the same coefficients in each case. Attention to this area was called in the early 1920's by R. D. Carmichael, who pointed out in addition the enormous variety of mixed…
  2. For many quantum-mechanical problems it is important to investigate the change of eigenvalues and eigenfunctions with the continuous change of one or more parameters. The case in which one knows the eigenvalues and eigenfunctions for two special values of the parameters, and is interested in the region in between is particularly interesting.

Etymology

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

This word in other languages

autovalor(Español)valeur propre(Français)Eigenwert(Deutsch)

Definitions, pronunciation, and etymology for this entry are drawn from Wiktionary via the kaikki.org structured extract (CC BY-SA); frequency ordering uses the FrequencyWords open word-frequency list (2018 English corpus, MIT). See the methodology for how each field is sourced and updated.

Frequently Asked Questions

How do you spell "eigenvalue"?
"eigenvalue" is spelled E-I-G-E-N-V-A-L-U-E. The IPA pronunciation is /ˈaɪ.ɡənˌvæl.juː/.
What does "eigenvalue" mean?
As a noun, "eigenvalue" means: 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 b...
How do you pronounce "eigenvalue"?
The IPA (International Phonetic Alphabet) transcription for "eigenvalue" is /ˈaɪ.ɡənˌvæl.juː/. Click the speaker icon on the pronunciation badge above to hear it spoken aloud where audio is available.
What is the origin of the word "eigenvalue"?
From eigen- + value. Partial calque of German Eigenwert. See the full etymology section above for more details.
Is PlainSpell free to use?
Yes, PlainSpell is a completely free word reference. You can look up definitions, pronunciations, confusable pairs, homophones, and spelling corrections across 5 languages without any sign-up or subscription.

Similar English words by spelling shape

Same letter count and similar misspelling depth for "eigenvalue", not the corpus desk frequency band.

Same letter count

Frequency-ranked English headwords with 10 letters (nearest by frequency rank).

dinnertime#60,768Fitzgibbon#60,809flagrantly#60,810desiccated#60,761

Source: Wiktionary (via kaikki.org) Structured Wiktionary extract

Source: FrequencyWords open word-frequency list