Vector Spaces and Linear Transformations
... If H is a subspace of V , then H is closed for the addition and scalar multiplication of V , i.e., for any u, v ∈ H and scalar c ∈ R, we have u + v ∈ H, cv ∈ H. For a nonempty set S of a vector space V , to verify whether S is a subspace of V , it is required to check (1) whether the addition and s ...
... If H is a subspace of V , then H is closed for the addition and scalar multiplication of V , i.e., for any u, v ∈ H and scalar c ∈ R, we have u + v ∈ H, cv ∈ H. For a nonempty set S of a vector space V , to verify whether S is a subspace of V , it is required to check (1) whether the addition and s ...
