16 янв. 2015 г. · A tensor is a vector of the tensor space T(m,n)(V), which is itself forms a vector space. A tensor space T(m,n)(V) is defined over a vector space V as the set ...

2 мая 2018 г. · The tensor product space is a space where the elements from each original space may be multiplied. This multiplication is distributive and allows different ...

24 июл. 2019 г. · Recall that the tensor product V⊗W of two finite-dimensional vector spaces V and W satisfy the dimension formula dim(V⊗W)=dim(V)⋅dim(W).

1 февр. 2019 г. · The first definition seems to be the definition of a tensor on a vector space while the second is a definition of tensor product of several ...

12 янв. 2013 г. · Here is another solution (from the notes that Keenan mentioned). Assume U and V are nonzero k-vector spaces. Pick nonzero vectors u0∈U and v0∈V.

9 мая 2014 г. · It's literally immediately from the definition of quotient. If V/W is a quotient space then for x∈V we have ˉx=0 in V/W iff x∈W.

19 мая 2014 г. · Every vector space over a field K is the direct sum of copies of K. (possibly zero copies, or even an infinite cardinal number of them).

2 мар. 2014 г. · I think tensors are by definition elements of the tensor product of vector spaces. Any vector space V over K is naturally isomorphic to V⊗K, ...

3 нояб. 2011 г. · Note that "dual basis" is a bit of a misleading notion here, since it will not be a basis of the dual space when V1⊗V2 is infinite-dimensional.

24 июл. 2019 г. · A tensor space is a quotient space w.r.t. to the smallest subspace which contains the defining equations of the tensors. There is no way to get ...