How Does the Length of a Kronecker Product Relate to Its Component Vectors?

[Dragonfall]

Suppose a, b are vectors in R^n, R^m resp. What can I say about the length of $$a\otimes b$$ wrt a and b?

You can think of $$\otimes$$ as the Kronecker product.

 

[Dragonfall]

Anyone?

 

[HallsofIvy]

How do you define the "length" of a tensor?

 

[Dragonfall]

Euclidean length.