Let (A, B) be two vector spaces, i.e., commutative groups with additional structure. What is the additional

Question:

Let $A, B$ be two vector spaces, i.e., commutative groups with additional structure. What is the additional structure? What are the additional relations between $x, x^{\prime}, x^{\prime \prime}$ in $A$ that are preserved by a vector-space homomorphism $h: A ightarrow B$ ?

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