Linear independence

v_{1}, \dots, v_{n}

are linearly independent when

a_{1} v_{1} + \dots + a_{n} v_{n} = 0

implies

a_{1} = \dots = a_{n} = 0

.

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Linear dependence

Vectors are linearly dependent when some nonzero choice of coefficients gives a vanishing linear combination.

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Linear independence by

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Linear independence is a concept in linear algebra that pertains to a set of vectors. A set of vectors is said to be linearly independent if no vector in the set can be expressed as a linear combination of the others. This means that there are no scalars (coefficients) such that a linear combination of the vectors results in the zero vector, unless all the coefficients are zero.

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Linear independence by

Ciro Santilli  40 Updated 2025-07-16

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