\[ \DeclareMathOperator{\supp}{supp} \]

Suppose \(\mathbb{K}\) is either \(\mathbb{R}\) or \(\mathbb{C}\). The support of a vector \(x\in \mathbb{K}^d\) is defined by

\[ \supp x = \{x_i \mid x_i\neq 0, i\in \{1,\ldots ,d\}\}. \]
Remarks
  • Sometimes \(\lvert \supp x\rvert\) is denoted by \(\lVert x\rVert_0\) and it is called the \(l_0\)-norm of \(x\). However, this is not a norm.