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www.jeremykun.com | ||
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djalil.chafai.net
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| | | | | The Girko circular law theorem states that if \( {X} \) is a \( {n\times n} \) random matrix with independent and identically distributed entries (i.i.d) of variance \( {1/n} \) then the empirical measure \[ \frac{1}{n}\sum_{i=1}^n\delta_{\lambda_i(X)} \] made with the eigenvalues of \( {X} \), converges, as the dimension \( {n} \) tends to infinity, to the uniform law... | |
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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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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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whatibroke.com
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| | | Let's take a look at what I've broken today | ||
