Linear Algebra Vs. Abstract Algebra
Here's the dirt on how these objects relate to one another:
Linear algebra is strictly a subset of abstract algebra. Nonetheless, it's worth mentioning that in a certain sense, vector spaces are "perverse" in an algebraic sense: vectors and scalars can't be added to each other, a lurid state of affairs sure to vex any universal algebraist.
To many students, an encounter with the notion of linear transformations in an elementary linear algebra course is the first sampling of the rich beauty of homomorphisms in general.
To many students, an encounter with the notion of linear transformations in an elementary linear algebra course is the first sampling of the rich beauty of homomorphisms in general.