Linear Span of a set : Linear Algebra : Degree #linear #span #of #a #set
Linear Span of a set : Let S be a non-empty subset of a vector space V (F). Then the set of all linear combinations of vectors of S is called the linear span of S and is denoted by L (S). i.e. L (S) = { 𝜶 / 𝜶 = 𝜮 , 1 ≤ i ≤ n } . For example : If S = { 𝜶 1 , 𝜶 2 , … , 𝜶 n .} and if 𝜶 𝞊 L (S) then there exist scalars a 1 , a 2 , … , a n such that 𝜶 = a 1 𝜶 1 +a 2 𝜶 2 + … +a n 𝜶 n . * Linear combination of vectors * linear sum of subspaces * What is a vector space * Theorem on vector space * Historical Introduction to Linear Algebra * Let V(F) be a vector space and let W ⊆ V. The necess...