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| | jasonmaa.com
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| | stephenmalina.com
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| | Selected Exercises # 5.A # 12. Define $ T \in \mathcal L(\mathcal P_4(\mathbf{R})) $ by $$ (Tp)(x) = xp'(x) $$ for all $ x \in \mathbf{R} $. Find all eigenvalues and eigenvectors of $ T $. Observe that, if $ p = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + a_4 x^4 $, then $$ x p'(x) = a_1 x + 2 a_2 x^2 + 3 a_3 x^3 + 4 a_4 x^4.
| | www.karlrupp.net
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| | [AI summary] A new Python library called PyViennaCL is introduced to provide efficient GPU-accelerated linear algebra and numerical computing capabilities compatible with NumPy and SciPy.
| | djalil.chafai.net
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| In this short post, we recall the pleasant notion of Fréchet mean (or Karcher mean) of a probability measure on a metric space, a concept already considered in an old previous post. Let \( {(E,d)} \) be a metric space, such as a graph (with vertices and edges) or a Riemannian manifold, equipped with its Borel \( {\sigma} \)-field. Let...