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www.randomservices.org | ||
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djalil.chafai.net
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| | | | | This post is mainly devoted to a probabilistic proof of a famous theorem due to Schoenberg on radial positive definite functions. Let us begin with a general notion: we say that \( {K:\mathbb{R}^d\times\mathbb{R}^d\rightarrow\mathbb{R}} \) is a positive definite kernel when \[ \forall n\geq1, \forall x_1,\ldots,x_n\in\mathbb{R}^d, \forall c\in\mathbb{C}^n, \quad\sum_{i=1}^n\sum_{j=1}^nc_iK(x_i,x_j)\bar{c}_j\geq0. \] When \( {K} \) is symmetric, i.e. \( {K(x,y)=K(y,x)} \) for... | |
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jonathanweisberg.org
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| | | | | Jonathan Weisberg's Homepage | |
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www.countbayesie.com
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| | | | | Learn about Discrete and Continuous probability distributions as well as the types of questions that they can both answers. This post also discusses the relationship between the Binomial and Beta distributions. | |
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nhigham.com
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| | | For a polynomial $latex \notag \phi(t) = a_kt^k + \cdots + a_1t + a_0, $ where $latex a_k\in\mathbb{C}$ for all $latex k$, the matrix polynomial obtained by evaluating $latex \phi$ at $latex A\in\mathbb{C}^{n \times n}$ is $latex \notag \phi(A) = a_kA^k + \cdots + a_1A + a_0 I. $ (Note that the constant term is... | ||
