Mathematics - Linear Algebra - Vector spaces and subspaces - What Is a Vector Space?

10 steps: (1) A vector space V is a set with addition and scalar multiplication satisfying 8 axioms. (2) Key axioms: closure under addition (u+v ∈ V), closure under scalar multiplication (cv ∈ V), zero vector exists. (3) Examples: ℝⁿ, space of polynomials of degree ≤n, space of continuous functions.