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

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Discussion Overview

The discussion centers on the relationship between the length of the Kronecker product of two vectors and the lengths of the individual vectors. Participants explore the concept of "length" in the context of the Kronecker product, specifically focusing on definitions and implications.

Discussion Character

  • Exploratory, Conceptual clarification

Main Points Raised

  • One participant inquires about the relationship between the length of the Kronecker product of two vectors, a and b, in R^n and R^m.
  • Another participant asks for clarification on how to define the "length" of a tensor, indicating a need for a more precise understanding of the term in this context.
  • A subsequent reply suggests that the "length" refers to Euclidean length, which may imply a specific interpretation of the term.

Areas of Agreement / Disagreement

The discussion does not reach a consensus on the definition of "length" or its implications for the Kronecker product, as participants are still seeking clarification and exploring the concept.

Dragonfall
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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.
 
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How do you define the "length" of a tensor?
 
Euclidean length.
 

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