Index of norms and absolute values

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This index is for:

  • [ilmath]\Vert\cdot\Vert[/ilmath]-like (which are norms) and
  • [ilmath]\vert\cdot\vert[/ilmath]-like (which are absolute values)



Expression Index Context Details
[math]\|\cdot\|[/math] [math]\|v\|[/math]
  • Functional Analysis
  • Real Analysis
Denotes the Norm of a vector
[math]\|\cdot\|_{C^k}[/math] [math]\|f\|_{C^k}[/math] CK
  • Functional Analysis
This Norm is defined by [math]\|f\|_{C^k}=\sum^k_{i=0}\sup_{t\in[0,1]}(|f^{(i)}(t)|)[/math] - note [math]f^{(i)}[/math] is the [math]i^\text{th}[/math] derivative.
[math]\|\cdot\|_\infty[/math] [math]\|f\|_\infty[/math] INFINITY
  • Functional Analysis
  • Real Analysis
It is a norm on [math]C([a,b],\mathbb{R})[/math], given by [math]\|f\|_\infty=\sup_{x\in[a,b]}(|f(x)|)[/math]
[math]\|\cdot\|_{L^p}[/math] [math]\|f\|_{L^p}[/math] LP
  • Functional Analysis
[math]\|f\|_{L^p}=\left(\int^1_0|f(t)|^pdt\right)^\frac{1}{p}[/math] - it is a Norm on [math]\mathcal{C}([0,1],\mathbb{R})[/math]

Absolute values

Expression Index Context Details
[math]|\cdot|[/math] [math]|x|[/math]
  • Real analysis
  • Abstract algebra
The traditional Absolute value