"direct sum" meaning in English

See direct sum in All languages combined, or Wiktionary

Noun

Forms: direct sums [plural]
Head templates: {{en-noun}} direct sum (plural direct sums)
  1. (mathematics) coproduct in some categories, like abelian groups, topological spaces or modules Categories (topical): Mathematics Translations (coproduct in some categories): suora summa (Finnish)
    Sense id: en-direct_sum-en-noun-JInnkFvg Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries, Terms with Finnish translations Disambiguation of English entries with incorrect language header: 42 33 25 Disambiguation of Entries with translation boxes: 40 37 23 Disambiguation of Pages with 1 entry: 41 33 26 Disambiguation of Pages with entries: 43 32 25 Disambiguation of Terms with Finnish translations: 39 30 30 Topics: mathematics, sciences Disambiguation of 'coproduct in some categories': 74 17 9
  2. (linear algebra) 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. Categories (topical): Linear algebra
    Sense id: en-direct_sum-en-noun-Quf2YWdA Categories (other): Entries with translation boxes, Pages with 1 entry Disambiguation of Entries with translation boxes: 40 37 23 Disambiguation of Pages with 1 entry: 41 33 26 Topics: linear-algebra, mathematics, sciences
  3. (linear algebra) A block diagonal matrix interpreted as having its non-zero blocks (which are square matrices) as summands. Categories (topical): Linear algebra
    Sense id: en-direct_sum-en-noun-BBvcrCmP Categories (other): Entries with translation boxes, Pages with 1 entry Disambiguation of Entries with translation boxes: 40 37 23 Disambiguation of Pages with 1 entry: 41 33 26 Topics: linear-algebra, mathematics, sciences

Inflected forms

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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.