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xorshammer.com | ||
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nhigham.com
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| | | | | A Householder matrix is an $latex n\times n$ orthogonal matrix of the form $latex \notag P = I - \displaystyle\frac{2}{v^Tv} vv^T, \qquad 0 \ne v \in\mathbb{R}^n. $ It is easily verified that $LATEX P$ is orthogonal ($LATEX P^TP = I$), symmetric ($LATEX P^T = P$), involutory ($LATEX P^2 = I$ that is, $LATEX P$ is... | |
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mathbabe.org
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| | | | | A continuation ofthis, where I take notes on my workshop atHCSSiM. The real numbers are uncountable Today we used Cantor's diagonal argument to prove that the real numbers aren't countable. Namely, we assumed they were, and that we had a bijection $latex f: \mathbb{N} \rightarrow \mathbb{R}$ and then proved it didn't contain the real number... | |
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fabricebaudoin.blog
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| | | | | Exercise 1.Solve Exercise 44 in Chapter 1 of the book. Exercise 2.Solve Exercise 3 in Chapter 1 of the book. Exercise 3.Solve Exercise 39 in Chapter 1 of the book. Exercise 4.The heat kernel on $latex \mathbb{S}^1$ is given by $latex p(t,y) =\frac{1}{2\pi}\sum_{m \in \mathbb{Z}} e^{-m^2 t} e^{im y} =\frac{1}{\sqrt{4\pi t}} \sum_{k \in \mathbb{Z}} e^{-\frac{(y... | |
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blog.computationalcomplexity.org
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| | | Hadi Esmaeilzadeh is the newest professor in the School of Computer Science at Georgia Tech. Hadi works in computer architecture and did s... | ||
