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• 10:25, 29 September 2026 Rongzhou talk contribs created page Vector space (Created page with "== Mathematical definition == Set $\mathbf{V}$ is a '''vector space''' over $\mathbb{F}$ if: 1. Are defined operations ** of addition: $\mathbf{V} \times \mathbf{V} \to \mathbf{V}$ ** of scalar multiplication: $\mathbb{F} \times \mathbf{V} \to \mathbf{V}$ 2. Are satisfied the properties ** Commutativity: $\forall u,v\in\mathbf{V},\; u+v=v+u$; ** Associativity: $\forall u,v,w\in\mathbf{V},\;\forall a,b\in\mathbb{F},\; (u+v)+w=u+(v+w)\;\land\;(ab)v=a(bv)$; ** Additive i...")