TeXipedia

parallel

Denotes parallel lines or vectors in mathematics and physics, or serves as a norm operator in advanced mathematics.

Overview

Essential in geometry, linear algebra, and physics for expressing relationships between lines, planes, or vectors that maintain a constant distance and never intersect.

  • Commonly used in geometric proofs and constructions to indicate parallel lines or planes
  • Appears in linear algebra to denote vector parallelism
  • Serves as a norm operator in functional analysis and advanced mathematical notation
  • Used in physics notation for describing parallel circuit components or parallel optical rays
  • Often appears in conjunction with other mathematical symbols to express complex geometric or algebraic relationships

Examples

Expressing parallel vectors in linear algebra.

a⃗∥b⃗\vec{a} \parallel \vec{b} 
\vec{a} \parallel \vec{b}

Denoting parallel lines in geometry.

l1∥l2l_1 \parallel l_2 
l_1 \parallel l_2

Representing the matrix norm.

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