Nearly everything in linear algebra has important geometric interpretations. In addition, a lot that works in the 3-space we live in (for the non-relativistic

Nearly everything in linear algebra has important geometric interpretations. In addition, a lot that works in the 3-space we live in (for the non-relativistic approximation) generalizes to linear algebra, vector spaces more generally, and, in particular, both Hilbert space and Banach space.