Linear algebra MOC

Vector space

A vector space or linear space over a Field of scalars is an abelian group together with an action of on that is distributive and linear. linalg Explicitly¹, for any and

A generalization is a Module, where the requirement that be a field is relaxed to a ring. Hence a vector space is just a module over a field. Another way to view vector spaces is as field actions on an abelian group.

Physical vectors

In physics, the term “vector” is sometimes used more narrowly than “element of a vector space”. See Proper vector, Pseudovector, Proper scalar, Pseudoscalar, Proper tensor, Pseudotensor.

---

tidy | sembr | en

Footnotes

1. 2008. Advanced Linear Algebra, p. 35 ↩