# Support of a vector

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.

• What do you mean by support? Can you give an example? – abiessu Sep 10 '13 at 15:09
• support of a vector is the number of non-zero elements in that vector. – TenaliRaman Sep 10 '13 at 15:09
• Why don't you post that as an answer? @TenaliRaman – Gigili May 11 '15 at 20:35
• – Gigili May 11 '15 at 20:35
• The wikipedia page for support functions is a good place to start. en.wikipedia.org/wiki/Support_(mathematics) – Aaron Dall Jan 15 '18 at 9:10

## 2 Answers

According to TenaliRaman, "support of a vector is the number of non-zero elements in that vector."

I posted it here for clarity.

Let $\mathbf{v}$ be an $n$-dimensional sign vector, i.e., a vector in $\{+,-,0\}^n$. The 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.