Vector Space
Informally, when we add or multiply vectors in a vector space, the result vector stay in the space. In other word, the linear combination of vectors in vector space is still in that vector space.
Definition
vector spaces are a set of objects
, called vectors, with the operations scalars multiplication and addition, and a special member zero , that satisfy the following properties: For any vectors
, , , and scalars , :
and (closure property) (commutativity) (associativity) s.t. s.t.
A vector space that is contained in another vector space is called a subspace. And the four fundamental subspaces are the most important subspaces to study.
Info
Every vector space is a metric space with