A double-stroke vertical bidirectional arrow serving as both a relation symbol and delimiter in mathematical logic and set theory.
Examples
Logical equivalence in a two-way implication
x > 0 \Updownarrow x^2 > 0
As a double-line delimiter in matrix notation
\left\Updownarrow\begin{matrix} a & b \\ c & d \end{matrix}\right\Updownarrow
Showing bidirectional correspondence between sets
\{x \in \mathbb{R} : x > 0\} \Updownarrow \{y \in \mathbb{R} : e^y > 1\}