TeXipedia

lVert

Represents a double vertical bar notation commonly used for mathematical norms and vector spaces.

Overview

Essential in advanced mathematics and theoretical physics for denoting norms, particularly in functional analysis and operator theory.

  • Frequently used to express vector norms and matrix norms
  • Common in describing distances in normed vector spaces
  • Appears in mathematical proofs and theorems involving bounded operators
  • Often paired with \rVert to enclose expressions, similar to absolute value notation but with distinct mathematical meaning

Examples

Computing the matrix norm of A.

∥A∥=∑i=1m∑j=1n∣aij∣2\lVert A \rVert = \sqrt{\sum_{i=1}^{m}\sum_{j=1}^{n} |a_{ij}|^2} 
\lVert A \rVert = \sqrt{\sum_{i=1}^{m}\sum_{j=1}^{n} |a_{ij}|^2}

Defining a vector norm in a functional analysis context.

∥x∥∞=max⁡i∣xi∣\lVert x \rVert_{\infty} = \max_{i} |x_i| 
\lVert x \rVert_{\infty} = \max_{i} |x_i|

Expressing the distance between two vectors using norm notation.

d(x,y)=∥x−y∥d(x,y) = \lVert x - y \rVert 
d(x,y) = \lVert x - y \rVert