Real coordinate space: A real coordinate space of dimension n, often represented as ℝn, is a coordinate space over the set of the n-tuples of real numbers (sequences of n real numbers) with component-wise addition and scalar multiplication. It forms a real vector space.
Subspace: A subspace of a vector (or coordinate) space V is a subset H of V, such that H is itself a vector space under the same operations of vector addition and scalar multiplication that are already defined on V.
Basis of a subspace: If V is a subspace of ℝn basis of V is a set of vectors, 𝕧 ≡ {v1,v2,…vk}, such that 𝕧 is the minimum set of vectors ...