Phrase guide

direct sum

noun · 4 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

coproduct in some categories, like abelian groups, topological spaces or modules

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

noun

Meaning 2

A linear sum in which the intersection of the summands has dimension zero. Equivalently, a linear sum of two subspaces, any vector of which can be expressed uniquely as a sum of two vectors: one vector belonging to the first subspace, and the other vector belonging to the second subspace.

Definition source: English Wiktionary via Wiktextract

Topics: linear-algebra, mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

3

noun

Meaning 3

A block diagonal matrix interpreted as having its non-zero blocks (which are square matrices) as summands.

Definition source: English Wiktionary via Wiktextract

Topics: linear-algebra, mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

4

noun

Meaning 4

a union of two disjoint sets in which every element is the sum of an element from each of the disjoint sets

Definition source: Princeton WordNet 3.0

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

Broader terms: union, sum, join

History

Etymology

No etymology was provided for this word.

Across languages

Translations

2 source translations are retained for this English entry.

  • Finnish: suora summa — coproduct in some categories
  • Polish: suma prosta — coproduct in some categories