TITLE: Support of a vector
QUESTION [7 upvotes]: What is the support of a signed vector? By signed vector, I mean a vector which is determined by considering the signs of the coefficients of the entries of another vector.

REPLY [5 votes]: Let $\mathbf{v}$ be an $n$-dimensional sign vector, i.e., a vector in $\{+,-,0\}^n$. The following is a natural partition of $[n]$ induced by $\mathbf{v}$.

$\mathbf{v}^+ = \{i \in [n] | v_i = +\}$
$\mathbf{v}^- = \{i \in [n] | v_i = -\}$
$\mathbf{v}^0 = \{i \in [n] | v_i = 0\}$

The support of $\mathbf{v}$ is the set $[n] \setminus \mathbf{v}^0 = \mathbf{v}^+ \cup \mathbf{v}^-$ consisting of all indices corresponding to nonzero entries in $\mathbf{v}$.
See page 8 of Oriented Matroids for the above definition and the wikipedia page for more generality.