Bilinear mappings, tensor products and p-summing operators

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Discussion Overview

The discussion centers around the concepts of bilinear mappings, tensor products, and p-summing operators, with a request for explanations suitable for an undergraduate audience familiar with basic linear algebra and functional analysis. Participants share resources and seek clarification on these mathematical topics.

Discussion Character

  • Exploratory, Homework-related

Main Points Raised

  • One participant requests a simplified explanation of bilinear maps, tensor products, and p-summing operators, along with examples.
  • Another participant suggests a book that covers the requested concepts, although they note it primarily addresses bilinear operations and maps.
  • A different participant mentions that for tensors, Greub's Linear Algebra might be a useful resource, indicating that tensor-related content may be found in his Multilinear Algebra book.
  • There is a suggestion for the original poster to share their current understanding of the topics to facilitate better assistance.
  • An additional participant provides a link to an older thread that contains further book recommendations on tensor products.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best resources or methods for explaining the concepts, and multiple suggestions and viewpoints are presented without resolution.

Contextual Notes

Some participants reference specific books and threads, indicating a reliance on external resources for deeper understanding, but the effectiveness of these resources remains subjective and unresolved.

Who May Find This Useful

Undergraduate students studying linear algebra and functional analysis, as well as individuals seeking to understand bilinear mappings, tensor products, and p-summing operators.

Trevor101
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Can somebody please explain bilinear maps, tensor products and p-summing operators in an easy-to-understand way. As though explaining to an undergraduate student who just knows basic linear algebra and basic functional analysis. And please give some nice examples to make the explanations more clear. It would be much appreciated. Thanks.
 
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I did not see anything in the book linked by Lang except bilinear operations and maps. For tensors, i.e. multilinear ones, you might try Greub's Linear Algebra, if you can find a copy of the second edition. Maybe after that the tensor stuff was put into a different book, his Multilinear Algebra. There have been hundreds of posts on tensors here over the last 9 years that I have been here, and you can search threads here quite well.

Here is one of them from 2004:

https://www.physicsforums.com/showthread.php?p=262170#post262170
 
Trevor101 said:
Can somebody please explain bilinear maps, tensor products and p-summing operators in an easy-to-understand way. As though explaining to an undergraduate student who just knows basic linear algebra and basic functional analysis. And please give some nice examples to make the explanations more clear. It would be much appreciated. Thanks.

Maybe you can meet us halfway by telling us what you understand about each and what you don't understand.
 

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