It's not uncommon for even undergraduate linear algebra to cover abstract spaces and notions of linearity which generalize beyond R^n. For example, the function space P_n consisting of all polynomials with degree less than or equal to n. Hoffman-Kunze, Halmos, Axler and Friedberg-Insel-Spence are all examples of undergraduate textbooks which cover this material.
This isn't just theoretical. Function spaces like P_n are useful in applied mathematics. And even if you don't use function spaces, it's very common for engineers, physicists and applied mathematicians to work in the complex space C^n rather than R^n.