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www.jeremykun.com | ||
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jiggerwit.wordpress.com
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| | | | | In the texbook I'm using for a first course in algebraic geometry, the proof of Bezout's theorem is awful. Looking around, I find an abundance of awful proofs. A good proof is one that I would want to commit to memory. Here is a good proof of Bezout's theorem, which is due to Gurjar and... | |
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xorshammer.com
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| | | | | There are a number of applications of logic to ordinary mathematics, with the most coming from (I believe) model theory. One of the easiest and most striking that I know is called Ax's Theorem. Ax's Theorem: For all polynomial functions $latex f\colon \mathbb{C}^n\to \mathbb{C}^n$, if $latex f$ is injective, then $latex f$ is surjective. Very... | |
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nhigham.com
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| | | | | The Cayley-Hamilton Theorem says that a square matrix $LATEX A$ satisfies its characteristic equation, that is $latex p(A) = 0$ where $latex p(t) = \det(tI-A)$ is the characteristic polynomial. This statement is not simply the substitution ``$latex p(A) = \det(A - A) = 0$'', which is not valid since $latex t$ must remain a scalar... | |
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localtvwhnt.wordpress.com
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