Bilinear mappings, tensor products and p-summing operators

[Trevor101]

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.

 

[micromass]

This book explains those concepts quite well: https://www.amazon.com/dp/1441930817/?tag=pfamazon01-20

 

[mathwonk]

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

 

[Bacle2]

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.

 

[mathwonk]

heres another old thread with lots of book suggestions:

https://www.physicsforums.com/showthread.php?t=39268&highlight=tensor+products