Vector spaces and linear algebra describe how structure emerges from direction, magnitude, and transformation. They form the backbone of geometry, physics, computation, and modern data science.
π¦ Definition & Axioms
π¦ Definition & Axioms
A vector space over a field π½ is a set equipped with vector addition and
scalar multiplication satisfying closure, associativity, distributivity,
identity, and inverses.
π’ Examples of Vector Spaces
π’ Examples of Vector Spaces
ββΏ, polynomial spaces, function spaces, and solution spaces of differential
equations all form vector spaces.