Index of notation/L

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Expression Status Meanings See also
(Linear Algebra)
[ilmath]L(V,W)[/ilmath] current Set of all linear maps, [ilmath](:V\rightarrow W)[/ilmath] - is a vector space in own right. Both vec spaces need to be over the same field, say [ilmath]\mathbb{F} [/ilmath].
[ilmath]L(V)[/ilmath] current Shorthand for [ilmath]L(V,V)[/ilmath] - see above
[ilmath]L(V,\mathbb{F})[/ilmath] current Space of all linear functionals, ie linear maps of the form [ilmath](:V\rightarrow\mathbb{F})[/ilmath] as every field is a vector space, this is no different to [ilmath]L(V,W)[/ilmath].
[ilmath]L(V_1,\ldots,V_k;W)[/ilmath] current All multilinear maps of the form [ilmath](:V_1\times\cdots\times V_k\rightarrow W)[/ilmath]
[ilmath]L(V_1,\ldots,V_k;\mathbb{F})[/ilmath] current Special case of [ilmath]L(V_1,\ldots,V_k;W)[/ilmath] as every field is a vector space. Has relations to the tensor product
[ilmath]\mathcal{L}(\cdots)[/ilmath] current Same as version above, with requirement that the maps be continuous, requires the vector spaces to be normed spaces (which is where the metric comes from to yield a topology for continuity to make sense)
(Measure Theory
Functional Analysis)
[ilmath]L^p[/ilmath] current
TODO: todo
[ilmath]\ell^p[/ilmath] current Special case of [ilmath]L^p[/ilmath] on [ilmath]\mathbb{N} [/ilmath]