Dyadic Tensor

Tensor Contraction - Contraction in Index Notation
... Since a general mixed dyadic tensor is a linear combination of decomposable tensors of the form, the explicit formula for the dyadic case follows let be a mixed dyadic tensor ... The resulting contracted tensor inherits the remaining indices of the original tensor ... For example, contracting a tensor T of type (2,2) on the second and third indices to create a new tensor U of type (1,1) is written as By contrast, let ...

Special Dyadics - Unit Dyadic
... For any vector a, there exist a unit dyadic I, such that For any basis of 3 vectors a, b and c, with reciprocal basis, the unit dyadic is defined by In the standard basis, The ... If V is a finite-dimensional vector space, a dyadic tensor on V is an elementary tensor in the tensor product of V with its dual space ... The tensor product of V and its dual space is isomorphic to the space of linear maps from V to V a dyadic tensor vf is simply the linear map sending any w in V to f(w)v ...