Timeline for Proving "almost all matrices over C are diagonalizable".
Current License: CC BY-SA 2.5
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| Jan 23, 2010 at 12:31 | comment | added | Pete L. Clark | Also recall the existence of space-filling curves over finite fields. Anyway, I think by now you take my point... | |
| Jan 23, 2010 at 12:28 | comment | added | Pete L. Clark | ... c.f. Exercise 21 of math.uga.edu/~pete/8320homework1.pdf | |
| Jan 23, 2010 at 12:26 | comment | added | Pete L. Clark | @KB: Here I meant the Zariski topology on $\mathbb{A}^n(k)$ -- I don't want to suggest scheme theory as a prerequisite for linear algebra! -- so that this is the discrete topology iff $k$ is finite. | |
| Jan 23, 2010 at 12:19 | comment | added | Kevin Buzzard | Pete: being a closed subset of A^n which isn't A^n is still a powerful statement when k is finite, because, as you well know, affine n-space over a finite field is still an infinite set. I once had to think twice about the following: "proper + quasi-finite implies finite, but projective 1-space over a finite field is proper and quasi-finite---umm---aah I see the point". | |
| Jan 23, 2010 at 9:57 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
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| Jan 22, 2010 at 18:35 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
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| Jan 22, 2010 at 18:11 | history | answered | Pete L. Clark | CC BY-SA 2.5 |