41. Where \ otimes is the tensor product , and \ oplus is the direct sum of vector spaces. 42. In algebraic number theory, tensor products of fields are ( implicitly, often ) a basic tool. 43. The Hilbert Schmidt operators form a two-sided naturally isometrically isomorphic to the tensor product of Hilbert spaces 44. The tensor product of two Hadamard transforms operating ( independently ) on two qubits is labelled H 2. 45. In principle, one could define a " tensor " simply to be an element of any tensor product . 46. The exterior product should not be confused with the outer product, which is the tensor product of vectors. 47. From here, through to the remainder of this article, the tensor product will always be explicitly shown. 48. The first case is a representation of the group product into the tensor product of the corresponding representation spaces. 49. In this case the action of \ gamma on an N-fold tensor product factors through the symmetric group 50. By a postulate of quantum mechanics, the state space of the composite system is given by the tensor product
