\lVert \rVert - LaTeX Symbol

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∥ ∥

\lVert \rVert

The \lVert and \rVert commands are used in LaTeX to create double vertical bars, often used to denote the norm of a vector or matrix. These delimiters are typically used in mathematical expressions to indicate the magnitude or length of a vector, or to represent the absolute value of a matrix.

Examples

∥ v ∥ = v_{1}^{2} + v_{2}^{2} + \dots + v_{n}^{2}

The norm of a vector \mathbf{v} in Euclidean space.

\lVert \mathbf{v} \rVert = \sqrt{v_1^2 + v_2^2 + \cdots + v_n^2}

∥ A ∥ = x \neq = 0 max \frac{∥ A x ∥}{∥ x ∥}

The operator norm of a matrix A.

\lVert A \rVert = \max_{\mathbf{x} \neq \mathbf{0}} \frac{\lVert A\mathbf{x} \rVert}{\lVert \mathbf{x} \rVert}

∥ f ∥_{L^{2}} = (\int ∣ f (x) ∣^{2} d x)^{1/2}

The L2 norm of a function f.

\lVert f \rVert_{L^2} = \left( \int |f(x)|^2 \, dx \right)^{1/2}