Definition – Linear basis. – Math-reference.net

Definition

Let $V$ be a vector space over some set $R$ . Let $X$ be a set of vectors in $V$ . We say that the set $X$ is a linear basis in $V$ if the following hold,

The set of vectors $X$ is linearly independent and,
Every vector in $V$ is equal to some linear combination of the vectors in $X$ .

Also see:

Every set of vectors in a finite dimensional vector space can be extended to a basis.