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|vector space |
A set of generalized vectors and a field of scalars, together with rules for their addition and multiplication (the same rules used for ordinary vectors and scalars).
An additive group on which some (scalar) field has an associative multiplicative action which distributes over the addition of the vector space and respects the addition of the (scalar) field: for vectors u, v and scalars h, k; h(u+v) = hu + hv; (h+k)u = hu + ku; (hk)u = h(ku).