Difference between revisions of "Index of norms and absolute values"
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Latest revision as of 09:16, 9 June 2015
This index is for:
- [ilmath]\Vert\cdot\Vert[/ilmath]-like (which are norms) and
- [ilmath]\vert\cdot\vert[/ilmath]-like (which are absolute values)
expressions
Contents
Norms
| Expression | Index | Context | Details | |
|---|---|---|---|---|
| [math]\|\cdot\|[/math] | [math]\|v\|[/math] |
|
Denotes the Norm of a vector | |
| [math]\|\cdot\|_{C^k}[/math] | [math]\|f\|_{C^k}[/math] | CK |
|
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 |
|
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 |
|
[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] |
|
The traditional Absolute value | |
