TeXipedia

lvert

Represents a single vertical bar delimiter used for absolute values, set notation, and mathematical norms.

Overview

Serves as a left vertical bar delimiter that pairs naturally with \rvert to create proper mathematical notation in formal writing. Unlike the standard keyboard vertical bar (|), this delimiter provides correct spacing and scaling in mathematical contexts.

  • Essential for properly typesetting absolute value notation
  • Used in set-builder notation to define sets
  • Common in linear algebra for matrix determinants and vector norms
  • Automatically adjusts size when used in displayed equations
  • Often preferred over the basic | character for professional mathematical typography

Examples

Defining absolute value of a complex number.

∣z∣=x2+y2\lvert z \rvert = \sqrt{x^2 + y^2} 
\lvert z \rvert = \sqrt{x^2 + y^2}

Specifying the magnitude of a vector.

∣v⃗∣=x2+y2+z2\lvert \vec{v} \rvert = \sqrt{x^2 + y^2 + z^2} 
\lvert \vec{v} \rvert = \sqrt{x^2 + y^2 + z^2}

Expressing the determinant of a 2×2 matrix.

∣abcd∣=ad−bc\lvert \begin{matrix} a & b \\ c & d \end{matrix} \rvert = ad - bc 
\lvert \begin{matrix} a & b \\ c & d \end{matrix} \rvert = ad - bc