在线性代数里，矢量空间的一组元素中，若没有矢量可用有限个其他矢量的线性组合所表示，则称为线性无关或线性独立（linearly independent），反之称为线性相关（linearly dependent）。例如在三维欧几里得空间R的三个矢量(1, 0, 0)，(0, 1, 0)和(0, 0, 1)线性无关。但(2, −1, 1)，(1, 0, 1)和(3, −1, 2)线性相关，因为第三个是前两个的和。

The vectors in a set are said to be linearly independent if the equation

can only be satisfied by for . This implies that no vector in the set can be represented as a linear combination of the remaining vectors in the set. In other words, a set of vectors is linearly independent if the only representations of 0 as a linear combination of its vectors is the trivial representation in which all the scalars a_i are zero.