Spectral gap

Spectral gap

In mathematics, the spectral gap is the difference between the two largest eigenvalues of a matrix or operator; alternately, it is sometimes taken as the smallest non-zero eigenvalue. Various theorems relate this difference to other properties of the system. See:

* Expander graph (discrete case)
* Poincaré inequality (continuous case)

ee also

* Spectral radius


Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • Spectral radius — In mathematics, the spectral radius of a matrix or a bounded linear operator is the supremum among the absolute values of the elements in its spectrum, which is sometimes denoted by rho;( middot;).pectral radius of a matrixLet lambda;1, hellip;,… …   Wikipedia

  • Mass gap — Quantum field theory (Feynman diagram) …   Wikipedia

  • Band gap — This article is about solid state physics. For voltage control circuitry in electronics, see Bandgap voltage reference. In solid state physics, a band gap, also called an energy gap or bandgap, is an energy range in a solid where no electron… …   Wikipedia

  • Hertzsprung gap — The Hertzsprung gap is a feature of the HR diagram for a star cluster. It is named after Ejnar Hertzsprung who first noticed the absence of stars in the region of the HR diagram between A5 and G0 spectral type and between +1 and 3 absolute… …   Wikipedia

  • Expander graph — In combinatorics, an expander graph is a sparse graph which has high connectivity properties, quantified using vertex or edge expansion as described below. Expander constructions have spawned research in pure and applied mathematics, with several …   Wikipedia

  • Discrete Laplace operator — For the discrete equivalent of the Laplace transform, see Z transform. In mathematics, the discrete Laplace operator is an analog of the continuous Laplace operator, defined so that it has meaning on a graph or a discrete grid. For the case of a… …   Wikipedia

  • List of mathematics articles (S) — NOTOC S S duality S matrix S plane S transform S unit S.O.S. Mathematics SA subgroup Saccheri quadrilateral Sacks spiral Sacred geometry Saddle node bifurcation Saddle point Saddle surface Sadleirian Professor of Pure Mathematics Safe prime Safe… …   Wikipedia

  • Eigengap — In linear algebra, the eigengap of a linear operator is the difference between two successive eigenvalues, where eigenvalues are sorted in ascending order. The Davis–Kahan theorem, named after Chandler Davis and William Kahan, uses the eigengap… …   Wikipedia

  • Null graph — In the mathematical field of graph theory, the null graph may refer either to the order zero graph, or alternatively, to any edgeless graph (the latter is sometimes called an empty graph). Contents 1 Order zero graph 2 Edgeless graph 3 See also …   Wikipedia

  • Ramanujan graph — A Ramanujan graph, named after Srinivasa Ramanujan, is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory). Such graphs are excellent spectral expanders.Examples of Ramanujan graphs include the clique,… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”