TeXipedia

Vert

Renders a double vertical bar symbol commonly used to denote matrix norms, vector norms, or absolute values in mathematical expressions.

Overview

Essential in linear algebra, functional analysis, and advanced mathematics for representing various types of norms and mathematical distances.

  • Frequently used to denote matrix and vector norms (e.g., L2-norm)
  • Appears in operator theory to represent operator norms
  • Common in mathematical proofs and theorems involving metric spaces
  • Often used to express the magnitude or length of vectors
  • Can be used to denote parallel lines in geometry when doubled

Examples

Expressing the norm of a vector

∥v⃗∥=x2+y2+z2\|\vec{v}\| = \sqrt{x^2 + y^2 + z^2} 
\|\vec{v}\| = \sqrt{x^2 + y^2 + z^2}

Defining a matrix norm

∥A∥=sup⁡x≠0∥Ax∥∥x∥\|A\| = \sup_{x \neq 0} \frac{\|Ax\|}{\|x\|} 
\|A\| = \sup_{x \neq 0} \frac{\|Ax\|}{\|x\|}

Showing parallel lines in geometry

L1∥L2  ⟺  ∥L1−L2∥>0L_1 \parallel L_2 \iff \|L_1 - L_2\| > 0 
L_1 \parallel L_2 \iff \|L_1 - L_2\| > 0