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Lagrange's identity is the algebraic identity (sum_(k=1)^na_kb_k)^2=(sum_(k=1)^na_k^2)(sum_(k=1)^nb_k^2)-sum_(1<=k<j<=n)(a_kb_j-a_jb_k)^2 (1) (Mitrinović 1970, p. 41; Marsden ...

The large Witt graph, also called the octad graph (Brouwer) or Witt graph (DistanceRegular.org), is the graph whose vertices are the 759 blocks of a Steiner system S(5,8,24) ...

Given a square complex or real matrix A, a matrix norm ||A|| is a nonnegative number associated with A having the properties 1. ||A||>0 when A!=0 and ||A||=0 iff A=0, 2. ...

Let G=(V,E) be a finite graph, let Omega be the set Omega={0,1}^E whose members are vectors omega=(omega(e):e in E), and let F be the sigma-algebra of all subsets of Omega. A ...

A smooth structure on a topological manifold (also called a differentiable structure) is given by a smooth atlas of coordinate charts, i.e., the transition functions between ...

A sutured manifold is a tool in geometric topology which was first introduced by David Gabai in order to study taut foliations on 3-manifolds. Roughly, a sutured manifold is ...

The theta series of a lattice is the generating function for the number of vectors with norm n in the lattice. Theta series for a number of lattices are implemented in the ...

Let V be a real symmetric matrix of large order N having random elements v_(ij) that for i<=j are independently distributed with equal densities, equal second moments m^2, ...

The Barth decic is a decic surface in complex three-dimensional projective space having the maximum possible number of ordinary double points, namely 345. It is given by the ...

Endraß surfaces are a pair of octic surfaces which have 168 ordinary double points. This is the maximum number known to exist for an octic surface, although the rigorous ...