These structures are the objects in the representative example of a compact closed category. Modules (15[1])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. Norms assign elements (10[1])of these structures to non-negative reals (10[1])and may be induced by an inner product. Linear maps are functions between these structures, which are closed under addition and scalar multiplication. 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■