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  • https://math.libretexts.org/Under_Construction/Purgatory/Remixer_University/Username%3A_junalyn2020/Book%3A_Introduction_to_Real_Analysis_(Lebl)/8%3A_Several_Variables_and_Partial_Derivatives/8.1%3A_Vector_Spaces%2C_linear_Mappings%2C_and_Convexity
    Let X be a set together with operations of addition, +:X×XX, and multiplication, :R×XX, (we write ax instead of ax). \(X...Let X be a set together with operations of addition, +:X×XX, and multiplication, :R×XX, (we write ax instead of ax). X is called a vector space (or a real vector space) if the following conditions are satisfied: (Addition is associative) If u,v,wX, then u+(v+w)=(u+v)+w. (Addition is commutative) If u,vX, then u+v=v+u. (Additive identity) There is a 0X such that v+0=v

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