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

Dragonfall
Messages
1,023
Reaction score
5
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.
 
Physics news on Phys.org
Anyone?
 
How do you define the "length" of a tensor?
 
Euclidean length.
 

Thread 'Trouble understanding an online solution to an exercise in Dummit & Foote'

##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Thread '##(A/\mathfrak{a})_{\mathfrak{p}/\mathfrak{a}}## and its isomorphism?'

I asked online questions about Proposition 2.1.1: The answer I got is the following: I have some questions about the answer I got. When the person answering says: ##1.## Is the map ##\mathfrak{q}\mapsto \mathfrak{q} A _\mathfrak{p}## from ##A\setminus \mathfrak{p}\to A_\mathfrak{p}##? But I don't understand what the author meant for the rest of the sentence in mathematical notation: ##2.## In the next statement where the author says: How is ##A\to...
View full post »

Similar threads

I Terminologies used to describe tensor product of vector spaces
Replies
7
Views
3K
I Composite quantum systems: Kronecker and Hadamard/Schur products
Replies
2
Views
2K
I Mapping tensor products into a Clifford algebra
Replies
7
Views
2K
A Tensor product matrices order relation
Replies
1
Views
1K
Kronecker product of infinite dimensional matrices
Replies
4
Views
4K
B Confused about dot product multiplication
Replies
33
Views
4K
I Taking the Tensor Product of Vectors
Replies
1
Views
2K
Example of an algebra tensor product
Replies
17
Views
3K
I Non orthogonal basis and the lines of its coordinate grid
Replies
9
Views
3K
I Is tensor product the same as dyadic product of two vectors?
Replies
4
Views
3K

Hot Threads

Recent Insights

Back
Top