# General Vector Spaces

#### matqkks

##### Member
Students familiar with Euclidean space find the introduction of general vectors spaces pretty boring and abstract particularly when describing vector spaces such as set of polynomials or set of continuous functions. Is there a tangible way to introduce this? Are there examples which will have a real impact? I would like to introduce this in an engaging manner to introductory students. Are there any real life applications of general vector spaces?

#### Fantini

Well, the definition of general vector spaces is an abstraction from the usual properties of $\mathbb{R}^n$. I'm not sure what kind of "real life" applications you could show. Almost everything usually is described using linear algebra, but you need additional information and structures for it to become interesting, like linear maps, decomposition into subspaces, etc. I don't think there'll be a vector space that's all useful just by existence.