TeXipedia

rVert

Represents a right vertical double bar delimiter, commonly used for mathematical norms and absolute values in advanced notation.

Overview

Serves as a specialized mathematical delimiter primarily found in advanced mathematical writing and theoretical papers where precise notation is crucial.

  • Essential for denoting specific types of norms, particularly in functional analysis and linear algebra
  • Often paired with \lVert to create matching pairs of double vertical bars
  • Frequently appears in contexts involving vector spaces, operator theory, and mathematical physics
  • Provides a more semantically correct alternative to using multiple vertical bars (||) when indicating norms

Examples

Computing the operator norm of a matrix A.

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

Defining a vector norm in a functional analysis context.

∥f∥L2=(∫ab∣f(x)∣2dx)1/2\rVert f \rVert_{L^2} = \left(\int_a^b |f(x)|^2 dx\right)^{1/2} 
\rVert f \rVert_{L^2} = \left(\int_a^b |f(x)|^2 dx\right)^{1/2}

Expressing the distance between two vectors in a normed space.

d(u,v)=∥u−v∥d(u,v) = \rVert u - v \rVert 
d(u,v) = \rVert u - v \rVert