---- > [!definition] Definition. ([[positive linear map]]) > If $[a,b]$ and $[c,d]$ are two [[closed interval|intervals]] in $\mathbb{R}$, there is a unique map $p:[a,b] \to [c,d]$ of the form $p(x)=mx + k$ that carries $a$ to $c$ and $b$ to $d$; we call it the **positive linear map** of $[a,b]$ to $[c,d]$. > \ > Note that the inverse of such a map is another such map. Same with compositions. Draw picture. ---- #### ---- #### References > [!backlink] > ```dataview TABLE rows.file.link as "Further Reading" FROM [[]] FLATTEN file.tags GROUP BY file.tags as Tag > [!frontlink] > ```dataview TABLE rows.file.link as "Further Reading" FROM outgoing([[]]) FLATTEN file.tags GROUP BY file.tags as Tag