This question came to me after discuss if there are nice examples of applied linear algerba topics in chemistry.
A chemical compound is often a bunch of less complex chemical compouds put together to react. Different amounts of some of these simpler compounds produce different final products. In this sense, I'd like to ask: is there something like getting an ''approximate'' final compound? More precisely, if a compound $c$ is not generated (by linear combinations) by simpler compounds $c_1,\ldots,c_k$, can we perform the least square method (or project the compound $c$ in the generated space by $c_1,\ldots,c_k$) and be ''chemically'' satisfyed with the result?