Explore >> Select a destination
|
You are here 
|
algassert.com | ||
| | | | |
nhigham.com
|
|
| | | | | 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... | |
| | | | |
quantumcomputinginc.com
|
|
| | | | | ||
| | | | |
fredrikj.net
|
|
| | | | | ||
| | | | |
djalil.chafai.net
|
|
| | | 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... | ||
