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Reference.org
Linear independence
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<p>In the theory of <a href="/facts/Vector_space/M1pxMLx2">vector spaces</a>, a <a href="/facts/Set_(mathematics)/BfucfHMq">set</a> of <a href="/facts/Vector_(mathematics)/U8mM7A5F">vectors</a> is said to be linearly independent if there exists no nontrivial <a href="/facts/Linear_combination/CVjL6kuN">linear combination</a> of the vectors that equals the zero vector. If such a linear combination exists, then the vectors are said to be linearly dependent. These concepts are central to the definition of <a href="/facts/Dimension_(vector_space)/z8m02A3W">dimension</a>. </p><p>A vector space can be of finite dimension or infinite dimension depending on the maximum number of linearly independent vectors. The definition of linear dependence and the ability to determine whether a subset of vectors in a vector space is linearly dependent are central to determining the dimension of a vector space. </p>