These structures are the objects in the representative example of a compact closed category. Modules are analogs to these structures defined over rings, and an algebra equips one of these structures with a bilinear product on a field. A representation is a group homomorphism from a group G to the automorphism group of one of these structures. The set of linear functionals on one of these structures forms [emphasize] another one of these structures called the (*) dual space. (10[1])Norms assign elements of these structures to non-negative reals and may be induced by an inner product. (-5[1])Linear maps are functions between these structures, which are closed under addition and scalar multiplication. (10[1])The number of elements of the basis of one of these structures gives their dimension. For 10 points, identify these sets consisting of objects that may have a magnitude and direction. ■END■ (0[1])