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The center of any sphere which has a contact of (at least) first-order with a curve C at a point P lies in the normal plane to C at P. The center of any sphere which has a ...

A permutation matrix is a matrix obtained by permuting the rows of an n×n identity matrix according to some permutation of the numbers 1 to n. Every row and column therefore ...

A radial function is a function phi:R^+->R satisfying phi(x,c)=phi(|x-c|) for points c in some subset Xi subset R^n. Here, |·| denotes the standard Euclidean norm in R^n and ...

Two square matrices A and B that are related by B=X^(-1)AX, (1) where X is a square nonsingular matrix are said to be similar. A transformation of the form X^(-1)AX is called ...

A solvable Lie group is a Lie group G which is connected and whose Lie algebra g is a solvable Lie algebra. That is, the Lie algebra commutator series ...

A Steiner system S(t,k,v) is a set X of v points, and a collection of subsets of X of size k (called blocks), such that any t points of X are in exactly one of the blocks. ...

Two submanifolds X and Y in an ambient space M intersect transversally if, for all p in X intersection Y, TX_p+TY_p={v+w:v in TX_p,w in TY_p}=TM_p, where the addition is in ...

The colon is the symbol ":". It is used in a number of different ways in mathematics. 1. To denote ratio or odds, as in 2:1 (voiced "two to one"). 2. To mean such that in ...

The group algebra K[G], where K is a field and G a group with the operation *, is the set of all linear combinations of finitely many elements of G with coefficients in K, ...

A hyperfunction, discovered by Mikio Sato in 1958, is defined as a pair of holomorphic functions (f,g) which are separated by a boundary gamma. If gamma is taken to be a ...