/sci/ - Science & Math » Thread #11398394

55KiB, 485x732, marty feldman.jpg

View Same Google iqdb SauceNAO

Anonymous Wed 19 Feb 08:04:10 2020 No.11398394 View Reply Original Report

Quoted By: >>11398425 >>11398505

Is every rank-n tensor a product of n vectors?

Anonymous

Anonymous Wed 19 Feb 2020 08:30:30 No.11398425 Report

Quoted By:

>>11398394
No. If that were the case, the tensor product wouldn't be a very interesting structure.

Anonymous

Anonymous Wed 19 Feb 2020 09:44:52 No.11398505 Report

Quoted By:

>>11398394
there is no common algebraic notion of rank in which that proposition holds.

you can construct counterexamples using type (p,q), p+q=2 tensors. e.g. any invertible map on a vector space of dimension at least 3.

Anonymous

Anonymous Wed 19 Feb 2020 11:34:33 No.11398663 Report

Quoted By: >>11400485

No. For example, in $\mathbb{R}^2 \otimes \mathbb{R}^2$ , $(0,1) \otimes (1,0) + (1,0)\otimes (0,1)$ is not a product of 2 vectors (Exercise: prove this).

Anonymous

Anonymous Wed 19 Feb 2020 23:53:49 No.11400485 Report

Quoted By:

>>11398663
based

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches