<human>:  How do you define a vector space?
<bot>: A vector space is a set of vectors. A vector is a mathematical object that has both a direction and a magnitude. A vector space is a set of vectors that have a certain property. For example, the set of all vectors in the plane is a vector space. The set of all vectors in the plane that have a magnitude of 1 is a subspace of the vector space of all vectors in the plane.