- #1
GR191511
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- TL;DR Summary
- Why is the tensor product of two tensors again a tensor?
> **Exercise.** Let T1and T2be tensors of type (r1 s1)and (r2 s2) respectively on a vector space V. Show that T1⊗
T2can be viewed as an (r1+r2 s1+s2)tensor, so that the
> tensor product of two tensors is again a tensor, justifying the
> nomenclature...
What I’m reading:《An introduction to tensors and group theory for physicists》Authors: Jeevanjee, Nadir. According to it,
a tensor is a multilinear function that eats r vectors as well as s dual vectors and produces a number...And "Give two finite-dimensional vector spaces V and W,we define their tensor product V⊗W to be the set of all C-valued bilinear functions on V*×W *..."
How do I define the tensor product of two tensors by these definition?And What the target object this tensor product acts on should look like?
T2can be viewed as an (r1+r2 s1+s2)tensor, so that the
> tensor product of two tensors is again a tensor, justifying the
> nomenclature...
What I’m reading:《An introduction to tensors and group theory for physicists》Authors: Jeevanjee, Nadir. According to it,
a tensor is a multilinear function that eats r vectors as well as s dual vectors and produces a number...And "Give two finite-dimensional vector spaces V and W,we define their tensor product V⊗W to be the set of all C-valued bilinear functions on V*×W *..."
How do I define the tensor product of two tensors by these definition?And What the target object this tensor product acts on should look like?