Explore >> Select a destination
|
You are here 
|
www.ethanepperly.com | ||
| | | | |
nhigham.com
|
|
| | | | | The trace of an $latex n\times n$ matrix is the sum of its diagonal elements: $latex \mathrm{trace}(A) = \sum_{i=1}^n a_{ii}$. The trace is linear, that is, $latex \mathrm{trace}(A+B) = \mathrm{trace}(A) + \mathrm{trace}(B)$, and $latex \mathrm{trace}(A) = \mathrm{trace}(A^T)$. A key fact is that the trace is also the sum of the eigenvalues. The proof is by... | |
| | | | |
francisbach.com
|
|
| | | | | ||
| | | | |
extremal010101.wordpress.com
|
|
| | | | | Suppose we want to understand under what conditions on $latex B$ we have $latex \begin{aligned} \mathbb{E} B(f(X), g(Y))\leq B(\mathbb{E}f(X), \mathbb{E} g(Y)) \end{aligned}$holds for all test functions, say real valued $latex f,g$, where $latex X, Y$ are some random variables (not necessarily all possible random variables!). If $latex X=Y$, i.e., $latex X$ and $latex Y$ are... | |
| | | | |
nhigham.com
|
|
| | | 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... | ||
