What is a linear embedding from a simplex $\Delta^n \to \mathbb{R}^n$?

Question

As stated in the title, reading Milnor-Stasheff Characteristic classes, I encountered at page 95 the following sentence:

let $\Delta^n$ be an $n$-simplex, linearly embedded in the $n$-dim vector space $V$ [...]

What is a linear embedding? The fact that $\Delta^n$ is not a vector space stops me from saying that it's a linear map, but I feel this should be the idea. I wasn't able to find anything on internet, so I'm asking here.

Answer 1

You can realize a simplex as $\{\,(x_1,\ldots,x_n)\in\mathbb R^n\mid x_i\ge 0; x_1+\ldots+x_n=1\,\}$ as a subset of $\mathbb R^n$ and consider linear maps defined on $\mathbb R^n$, restricted to the simplex.