I am studying a little bit of Convex Analysis, especially the structure of the closed convex sets (in French). I came across a term that kind of confused me which is "espace vectoriel augmenté" or "augmented vector space". It is defined as following:
Let $E$ be a vector space with a finite demension. Let $\hat{E}=E\oplus\mathbb{R}$ be the augmented vector space.
What does the name even mean? Is it like augmenting the demension of $E$?
Thanks in advance for your replies!