Timeline for Vector spaces without natural bases
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Jul 20, 2010 at 9:42 | comment | added | The Mathemagician | Once again,better mathematical living through The Axiom of Choice. | |
| Jul 18, 2010 at 23:57 | comment | added | Qiaochu Yuan | Very good point. Perhaps I should have said "the vector space of regular functions on the affine line." Then the point I'm trying to make with comment 1) is that the affine line is homogeneous with respect to its automorphism group. | |
| Jul 18, 2010 at 23:44 | comment | added | Johannes Hahn | Well the same could be said about any other "natural basis". It always comes down to privileging one basis over all other basis. From the viewpoint of pure linear algebra, there are no natural basis at all (excluding the empty set as the only and hence natural basis of the zero vector space). All basis are equal if one doesn't specify a point of view that comes from outside linear algebra. To decide whether some item is "natural" always requires knowledge on what you want to do with it. If I only want to test equality of explicitly given polynoms the basis (x^k) could be called natural. | |
| Jul 18, 2010 at 22:54 | history | answered | Qiaochu Yuan | CC BY-SA 2.5 |