Linear Sum of Subspaces : Linear Algebra : Degree
Linear Sum of Subspaces: Definition Let W 1 and W 2 be two subspaces of the vector space V(F) . Then the linear sum of the subspaces W 1 & W 2 , denoted by W 1 + W 2 , is the set of all sums 𝜶 1 + 𝜶 2 such that 𝜶 1 𝞊 W 1 , 𝜶 2 𝞊 W 2 i.e. W 1 + W 2 = { 𝜶 1 + 𝜶 2 / 𝜶 1 𝞊 W 1 , 𝜶 2 𝞊 W 2 }. * 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 necessary and sufficient conditions for W to be a subspace of V are (i) 𝜶 𝞊 W, 𝞫 𝞊 W ⇒ 𝜶 - 𝞫 𝞊 W ...