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www.ethanepperly.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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nhigham.com
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| | | | | A QR factorization of a rectangular matrix $latex A\in\mathbb{R}^{m\times n}$ with $latex m\ge n$ is a factorization $LATEX A = QR$ with $latex Q\in\mathbb{R}^{m\times m}$ orthonormal and $latex R\in\mathbb{R}^{m\times n}$ upper trapezoidal. The $LATEX R$ factor has the form $latex R = \left[\begin{smallmatrix}R_1\\ 0\end{smallmatrix}\right]$, where $LATEX R_1$ is $latex n\times n$ and upper triangular. Partitioning... | |
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nhigham.com
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| | | | | For an $latex n\times n$ matrix $latex \notag A = \begin{bmatrix} A_{11} & A_{12} \\ A_{21} & A_{22} \end{bmatrix} \qquad (1) $ with nonsingular $latex (1,1)$ block $LATEX A_{11}$ the Schur complement is $LATEX A_{22} - A_{21}A_{11}^{-1}A_{12}$. It is denoted by $LATEX A/A_{11}$. The block with respect to which the Schur complement is taken need... | |
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123ash.wordpress.com
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| | | By CDF, I mean Cumulative distribution function and by PDF, I mean probability density function. These are related to each other and are very important in understanding statistics and probability. I came across these terms while I was plotting a histogram of temperatures in Houston and Chicago. Normally, when we have some data, we can... | ||
