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Abstractly, the tensor direct product is the same as the vector space tensor product. However, it reflects an approach toward calculation using coordinates, and indices in ...

Suppose that V is a group representation of G, and W is a group representation of H. Then the vector space tensor product V tensor W is a group representation of the group ...

The tensor product of two vector spaces V and W, denoted V tensor W and also called the tensor direct product, is a way of creating a new vector space analogous to ...

The direct product is defined for a number of classes of algebraic objects, including sets, groups, rings, and modules. In each case, the direct product of an algebraic ...

The graph tensor product, also called the graph cardinal product (Imrich 1998), graph categorical product, graph conjunction, graph direct product (Hammack et al. 2016), ...

Given vectors u and v, the vector direct product, also known as a dyadic, is uv=u tensor v^(T), where tensor is the Kronecker product and v^(T) is the matrix transpose. For ...

Given two groups G and H, there are several ways to form a new group. The simplest is the direct product, denoted G×H. As a set, the group direct product is the Cartesian ...

The tensor product between modules A and B is a more general notion than the vector space tensor product. In this case, we replace "scalars" by a ring R. The familiar ...

The direct product of the rings R_gamma, for gamma some index set I, is the set product_(gamma in I)R_gamma={f:I-> union _(gamma in I)R_gamma|f(gamma) in R_gamma all gamma in ...

The term external direct product is used to refer to either the external direct sum of groups under the group operation of multiplication, or over infinitely many spaces in ...