Standard Lemma guide

diagonalize

verb · 3 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

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No pronunciation record was provided for this word.

1

verb

Meaning 1

To convert a square matrix into a diagonal matrix by multiplying it by a second matrix and its inverse.

Definition source: English Wiktionary via Wiktextract

Usage: transitive

Topics: mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

verb

Meaning 2

To design variables such that design problems only bear upon subsets that are loosely coupled to others.

Definition source: English Wiktionary via Wiktextract

Qualifier: cybernetics

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

3

verb

Meaning 3

transform a matrix to a diagonal matrix

Definition source: Princeton WordNet 3.0

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: diagonalise

Antonyms: none provided

Broader terms: translate, transform

History

Etymology

Etymology tree English diagonal Proto-Indo-European *-id- Proto-Indo-European *-yéti Proto-Indo-European *-idyéti Proto-Hellenic *-íďďō Ancient Greek -ῐ́ζω (-ĭ́zō)bor. Late Latin -izōder. Middle French -iserbor. Middle English -isen English -ize English diagonalize From diagonal + -ize.

Across languages

Translations

3 source translations are retained for this English entry.

  • Dutch: diagonaliseren — convert square matrix into diagonal matrix
  • Latin: diagōnālizō — convert square matrix into diagonal matrix
  • Spanish: diagonalizar — convert square matrix into diagonal matrix