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.
📦 Definition & Axioms
📦 Definition & Axioms
A vector space over a field 𝔽 is a set equipped with vector addition and
scalar multiplication satisfying closure, associativity, distributivity,
identity, and inverses.
🔢 Examples of Vector Spaces
🔢 Examples of Vector Spaces
ℝⁿ, polynomial spaces, function spaces, and solution spaces of differential
equations all form vector spaces.