| an additive group in which addition is commutative and with which is associated a field of scalars, as the field of real numbers, such that the product of a scalar and an element of the group or a vector is defined, the product of two scalars times a vector is associative, one times a vector is the vector, and two distributive laws hold. |
| vector space n. A system consisting of a set of generalized vectors and a field of scalars, having the same rules for vector addition and scalar multiplication as physical vectors and scalars. |
| 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). |
vector space mathematics
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).
[Simple example?]
(1996-09-30)
