X-Nico

SmallBASIC

SmallBASIC is also intended as a tool for mathematics, with built-in functions for Unit conversion, Algebra, Matrix math, Trigonometry, Statistics, and for two and three dimensional Equation Graphing.

see also

Attractor network

Bidirectional networks are similar to Hopfield networks, with the special case that the matrix $W$ is a block matrix.

Curvature of Riemannian manifolds

The curvature of n-dimensional Riemannian manifold is given by an antisymmetric n×n matrix $\backslash Omega^\{\}\; \{\}=\backslash Omega^i\; \{\backslash \; j\}$ of 2-forms (or equivalently a 2-form with values in $so(n)$, the Lie algebra of the orthogonal group $O(n)$, which is the structure group of the tangent bundle of a Riemannian manifold).

Dmrg of Heisenberg model

Diagonalize $\backslash rho$ and form the $m\backslash times\; (d*3)$ matrix $T$, which rows are the $m$ eigenvectors associated with the $m$ largest eigenvalue $e\; \backslash alpha$ of $\backslash rho$.

Lindblad equation

The coefficient matrix $\backslash \; h\; =\; (h\; \{n,m\})$ must be positive to ensure that the equation is trace-preserving and completely positive.