Linearly_independent
Definition
A list $v_{1},\ldots,v_{m}$ of vectors $V$ is called linearly independent if the only choice of $a_{1},\ldots,a_{m} \in \mathbb{F}$ that makes $a_{1}v_{1} + \cdots + a_{m}v_{m}$ equal 0 is $a_{1} = \cdots = a_{m} = 0$.
The empty list () is also declared to be linearly independent.
Theorem 2.23 (Axler): Length of linearly independent list $\leq$ length of spanning list
In a finite-dimensional_vector_space, the length of every linearly_independent list of vectors is less than or equal to the length of every spanning list of vectors.