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The invertible matrix theorem is a theorem in linear algebra which gives a series of equivalent conditions for an n×n square matrix A to have an inverse. In particular, A is ...

Let R[z]>0, 0<=alpha,beta<=1, and Lambda(alpha,beta,z)=sum_(r=0)^infty[lambda((r+alpha)z-ibeta)+lambda((r+1-alpha)z+ibeta)], (1) where lambda(x) = -ln(1-e^(-2pix)) (2) = ...

The Minkowski metric, also called the Minkowski tensor or pseudo-Riemannian metric, is a tensor eta_(alphabeta) whose elements are defined by the matrix (eta)_(alphabeta)=[-1 ...

The group Gamma of all Möbius transformations of the form tau^'=(atau+b)/(ctau+d), (1) where a, b, c, and d are integers with ad-bc=1. The group can be represented by the 2×2 ...

A beautiful general theorem of which the following two statements are special cases (Coxeter and Greitzer 1967, pp. 99-100). 1. If DeltaABC and DeltaA^'B^'C^' are two ...

If f:D->Y is a map (a.k.a. function, transformation, etc.) over a domain D, then the range of f, also called the image of D under f, is defined as the set of all values that ...

Special affine curvature, also called as the equi-affine or affine curvature, is a type of curvature for a plane curve that remains unchanged under a special affine ...

A transformation consisting of a constant offset with no rotation or distortion. In n-dimensional Euclidean space, a translation may be specified simply as a vector giving ...

Spinor fields describing particles of zero rest mass satisfy the so-called zero rest mass equations. Examples of zero rest mass particles include the neutrino (a fermion) and ...

Legendre showed that there is no rational algebraic function which always gives primes. In 1752, Goldbach showed that no polynomial with integer coefficients can give a prime ...