/explore
|
You are here 
|
nhigham.com | ||
| | | | |
nickhar.wordpress.com
|
|
| | | | | 1. Low-rank approximation of matrices Let $latex {A}&fg=000000$ be an arbitrary $latex {n \times m}&fg=000000$ matrix. We assume $latex {n \leq m}&fg=000000$. We consider the problem of approximating $latex {A}&fg=000000$ by a low-rank matrix. For example, we could seek to find a rank $latex {s}&fg=000000$ matrix $latex {B}&fg=000000$ minimizing $latex { \lVert A - B... | |
| | | | |
djalil.chafai.net
|
|
| | | | | Let $X$ be an $n\times n$ complex matrix. The eigenvalues $\lambda_1(X), \ldots, \lambda_n(X)$ of $X$ are the roots in $\mathbb{C}$ of its characteristic polynomial. We label them in such a way that $\displaystyle |\lambda_1(X)|\geq\cdots\geq|\lambda_n(X)|$ with growing phases. The spectral radius of $X$ is $\rho(X):=|\lambda_1(X)|$. The singular values $\displaystyle s_1(X)\geq\cdots\geq s_n(X)$ of $X$ are the eigenvalues of the positive semi-definite Hermitian... | |
| | | | |
djalil.chafai.net
|
|
| | | | | This post is devoted to certain properties of random permutation matrices. Let \( {\mathfrak{S}_n} \) be the symmetric group, \( {n\geq2} \), and let \( {\mathcal{P}_n} \) be the group of \( {n\times n} \) permutation matrices, obtained by the isomorphism \( {\sigma\in\mathfrak{S}_n\mapsto P_\sigma={(\mathbf{1}_{j=\sigma(i)})}_{1\leq i,j\leq n}} \). We know that \( {\mathcal{P}_n} \) is a subgroup of the orthogonal group... | |
| | | | |
arnavdhamija.com
|
|
| | | [AI summary] A technical blog post introduces Model Predictive Control, explaining its roots in chemical processing, its mathematical formulation using discrete systems and cost functions, and its application to robotics and autonomous vehicles. | ||
