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Linear independence

In linear algebra, a set of vectors is said to be linearly independent if there exists no vector in the set that is equal to a linear combination of the other vectors in the set. If such a vector exists, then the vectors are said to be linearly dependent. Linear independence is part of the definition of linear basis.

Art, Definition & Evaluating linear independence

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Definition

Vector spaceScalarsSubsetIndexed familySpans
8 related topics

Evaluating linear independence

If and only ifRow reduceDeterminantMatrix
4 related topics

Space of linear dependencies

Linear relationTupleSystem of linear equationsGaussian elimination
4 related topics

Generalizations

Affine combinationDirect sum
2 related topics

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Definition

Geometric examples

Evaluating linear independence

Natural basis vectors

Linear independence of functions

Space of linear dependencies

Generalizations

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Linear independence

Nodes35
Edges34
Triples12
Avg. degree1.94
Density0.057143
Components1

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Linear independence

Top relations

related to External links · 9
Linear independence → EMS Press, Encyclopedia, Introduction, KhanAcademy, Linear, Linearly Dependent Functions, Mathematics, Tutorial, WolframMathWorld
see also · 2
Linear independence → Abstraction, Matroid
part of · 1
Linear independence → the definition of linear basis

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Important terminology

displaystyle linearly vectors independent vector dependent linear mathbf set space zero sequence combination said one true case basis subset independence

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Linear independencepart ofthe definition of linear basis0.85text
Linear independencerelated to External linksLinear0.60section
Linear independencerelated to External linksEncyclopedia0.60section
Linear independencerelated to External linksMathematics0.60section
Linear independencerelated to External linksEMS Press0.60section
Linear independencerelated to External linksLinearly Dependent Functions0.60section
Linear independencerelated to External linksWolframMathWorld0.60section
Linear independencerelated to External linksTutorial0.60section
Linear independencerelated to External linksIntroduction0.60section
Linear independencerelated to External linksKhanAcademy0.60section
Linear independencesee alsoMatroid0.60section
Linear independencesee alsoAbstraction0.60section

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