Timeline for The meaning and purpose of "canonical''
Current License: CC BY-SA 4.0
4 events
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| Feb 27, 2020 at 20:23 | comment | added | LSpice | @FredRohrer, the problems is what kind of object $K^n$ is—or, perhaps to phrase it differently, how many automorphisms we allow it. As a bare vector space (with a full $\operatorname{GL}_n(K)$ of automorphisms), it's probably not reasonable to call the standard basis canonical, since it's not preserved by automorphisms. As a product of copies of $K$ indexed by the cardinal $n$, it has no non-trivial automorphisms, and the standard basis can reasonably be identified as a canonical choice. Bourbaki is careful, but can still make mistakes, or—if that is too strong—infelicities. | |
| Feb 27, 2020 at 20:15 | comment | added | Fred Rohrer | Well, Bourbaki, who is known for careful use of words, writes canonical basis for what you call standard basis. | |
| Feb 27, 2020 at 20:11 | history | edited | anon | CC BY-SA 4.0 |
added 93 characters in body
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| Feb 27, 2020 at 20:05 | history | answered | anon | CC BY-SA 4.0 |