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rjlipton.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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njwildberger.com
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| | | | | This semester I have been on Long Service Leave, so I am off the hook for teaching, and can spend more time with my graduate students Ali Alkhaldi and Nguyen Le, do some investigations into hyperbolic geometry and related issues, make more videos, and do some travelling. Ali is in his fourth year of the... | |
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anuragbishnoi.wordpress.com
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| | | | | The Ramsey number $latex R(s, t)$ is the smallest $latex n$ such that every graph on $latex \geq n$ vertices either contains a clique of size $latex s$ or an independent set of size $latex t$. Ramsey's theorem implies that these numbers always exist, and determining them (precisely or asymptotically) has been a major challenge... | |
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lucatrevisan.wordpress.com
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| | | A question that I am very interested in is whether it is possible to study hypergraphs with techniques that are in the spirit of spectral graph theory. It is generally possible to ``flatten'' the adjacency tensor of a hypergraph into a matrix, especially if the hypergraph is $latex {k}&fg=000000$-uniform with $latex {k}&fg=000000$ even, and spectral... | ||
