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A special nonsingular map from one manifold to another such that at every point in the domain of the map, the derivative is an injective linear transformation. This is ...

Jung's theorem states that the generalized diameter D of a compact set X in R^n satisfies D>=Rsqrt((2(n+1))/n), where R is the circumradius of X (Danzer et al. 1963). This ...

The Kreisel conjecture is a conjecture in proof theory that postulates that, if phi(x) is a formula in the language of arithmetic for which there exists a nonnegative integer ...

The multinomial coefficients (n_1,n_2,...,n_k)!=((n_1+n_2+...+n_k)!)/(n_1!n_2!...n_k!) (1) are the terms in the multinomial series expansion. In other words, the number of ...

A group that coincides with its commutator subgroup. If G is a non-Abelian group, its commutator subgroup is a normal subgroup other than the trivial group. It follows that ...

A pseudoinverse is a matrix inverse-like object that may be defined for a complex matrix, even if it is not necessarily square. For any given complex matrix, it is possible ...

A rhombohedron is a parallelepiped bounded by six rhombi such that opposite faces are congruent. A rhombohedron having all six rhombic faces congruent is known as a trigonal ...

A special graph vertex that is designated to turn a tree into a rooted tree or a graph into a rooted graph. The root is sometimes also called "eve," or an "endpoint" (Saaty ...

Every smooth manifold M has a tangent bundle TM, which consists of the tangent space TM_p at all points p in M. Since a tangent space TM_p is the set of all tangent vectors ...

A module having only one element: the singleton set {*}. It is a module over any ring R with respect to the multiplication defined by a*=* (1) for every a in R, and the ...