Question

what is a vector subspace?

Answer 1

Any subset of vectors of a larger group that are still closed under addition and scalar.

Answer 2

A subset of a vector space is a vector subspace of if the following two axioms are satisfied

S1 If and are vectors in , then so is ; and
S2 For any scalar , if is any vector in , then so is .
One also often uses the phrases ‘ ’ is a subspace of ’ and ‘ ’ is a linear subspace of ‘ .’