Linear Algebra in curved space We know that Euclidean geometry and Newtonian Physics are special cases that only work in a flat space-time. Got to thinking about linear algebra and matrices. Is linear-algebra a special subset of some math? And does LA only work because our local space-time is flat enough to discard any discrepancies that would result from plotting a "line" or a "plane" in a curved space-time?

The keyword is _Linearization_. Since anything in Physics is an approximation, things that are not linear, from a foundational point of view, may nevertheless be considered _as if they were linear_ , as a first approximation. Especially in technological applications, where robustness is more important than exactness (e.g. classical electronics), this is common practice. See: Linearization (Wikipedia).