# Symbols:L

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## Roman Numerals

$\mathrm L$

The Roman numeral for $50$.

Its $\LaTeX$ code is \mathrm L .

## The Set of All Linear Transformations

Let $G$ and $H$ be $R$-modules.

Then $\operatorname{Hom}_R \left({G, H}\right)$ is the set of all linear transformations from $G$ to $H$:

$\operatorname{Hom}_R \left({G, H}\right) := \left\{{\phi: G \to H: \phi \mbox{ is a linear transformation}}\right\}$

If it is clear (and therefore does not need to be stated) that the scalar ring is $R$, then this can be written $\operatorname{Hom} \left({G, H}\right)$.

Similarly, $\operatorname{Hom}_R \left({G}\right)$ is the set of all linear operators on $G$:

$\operatorname{Hom}_R \left({G}\right) := \left\{{\phi: G \to G: \phi \text{ is a linear operator}}\right\}$

Again, this can also be written $\operatorname{Hom} \left({G}\right)$.

The $\LaTeX$ code for $\mathcal L_R \left({G, H}\right)$ is \mathcal L_R \left({G, H}\right) .

The $\LaTeX$ code for $\mathcal L \left({G, H}\right)$ is \mathcal L \left({G, H}\right) .

The $\LaTeX$ code for $\mathcal L_R \left({G}\right)$ is \mathcal L_R \left({G}\right) .

The $\LaTeX$ code for $\mathcal L \left({G}\right)$ is \mathcal L \left({G}\right) .

### Note

The usual notation for the set of linear transformations involves use of the mathscript font, that is: $\mathscr L$, whose $\LaTeX$ code is \mathscr L, but this does not render in many versions of $\LaTeX$.

Since this site migrated to MathJax, it has become possible to use the $\mathscr L$. However, this has not yet been imnplemented.