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