Standard Lemma guide

diagonalisation

noun · 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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1

noun

Meaning 1

In matrix algebra, the process of converting a square matrix into a diagonal matrix, usually to find the eigenvalues of the matrix.

Definition source: English Wiktionary via Wiktextract

Usage: countable, uncountable

Topics: mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

noun

Meaning 2

An argument used in proof by contradiction by constructing a supposedly exhaustive list of all members of a class, and then subsequently constructing a new member which differs from each existing member in at least one place and therefore cannot belong to the list.

Definition source: English Wiktionary via Wiktextract

Usage: countable, uncountable

Topics: mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

3

noun

Meaning 3

changing a square matrix to diagonal form (with all non-zero elements on the principal diagonal)

Definition source: Princeton WordNet 3.0

Examples

  • the diagonalization of a normal matrix by a unitary transformation

Meaning relationships

Synonyms: diagonalization

Antonyms: none provided

Broader terms: resolution, resolving

History

Etymology

From diagonal + -isation.