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.
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1What do you mean by support? Can you give an example? – abiessu Sep 10 '13 at 15:09
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3support of a vector is the number of non-zero elements in that vector. – TenaliRaman Sep 10 '13 at 15:09
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Why don't you post that as an answer? @TenaliRaman – Gigili May 11 '15 at 20:35
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related: ℓ0 Minimization (Minimizing the support of a vector) – Gigili May 11 '15 at 20:35
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The wikipedia page for support functions is a good place to start. https://en.wikipedia.org/wiki/Support_(mathematics) – Aaron Dall Jan 15 '18 at 09:10
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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.
Aaron Dall
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According to TenaliRaman, "support of a vector is the number of non-zero elements in that vector."
I posted it here for clarity.
ARK
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