Phrase guide

linear independence

noun · 1 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.

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Pronunciation

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1

noun

Meaning 1

the state of being linearly independent

Definition source: English Wiktionary via Wiktextract

Usage: uncountable

Topics: algebra, mathematics, sciences

Examples

  • The linear independence of a set of vectors can be determined by calculating the Gram determinant of those vectors; if their Gram determinant is zero, then they are linearly dependent, and if their Gram determinant is non-zero, then they are linearly independent. Incidentally, the same Gram determinant can be used to calculate the hyper-volume of a hyper-parallelepiped (whose edges which "radiate" from an "origin" vertex are described by the vectors).

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.

Across languages

Translations

3 source translations are retained for this English entry.

  • Danish: lineær uafhængighed — state of being linearly independent
  • Portuguese: independência linear — state of being linearly independent
  • Spanish: independencia lineal — state of being linearly independent