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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.

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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.

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  • $\begingroup$ ok so a linear embedding is a restriction of a linear map to it, or equivalently a map which can be extended to a linear map between vector spaces? Because it seems somewhat restrictive the fact that comes from something defined globally let's say $\endgroup$
    – Luigi M
    Jun 15, 2015 at 21:01

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