Search Results for ""

A bilinear form on a real vector space is a function b:V×V->R that satisfies the following axioms for any scalar alpha and any choice of vectors v,w,v_1,v_2,w_1, and w_2. 1. ...

A cusp form is a modular form for which the coefficient c(0)=0 in the Fourier series f(tau)=sum_(n=0)^inftyc(n)e^(2piintau) (1) (Apostol 1997, p. 114). The only entire cusp ...

An expression that is of a given type. For example, all primes p>3 are "of the form" 6n+/-1. The term "of shape" is sometimes also used.

Angle addition formulas express trigonometric functions of sums of angles alpha+/-beta in terms of functions of alpha and beta. The fundamental formulas of angle addition in ...

A matrix that has undergone Gaussian elimination is said to be in row echelon form or, more properly, "reduced echelon form" or "row-reduced echelon form." Such a matrix has ...

Let M be a regular surface with v_(p),w_(p) points in the tangent space M_(p) of M. Then the first fundamental form is the inner product of tangent vectors, ...

A differential k-form can be integrated on an n-dimensional manifold. The basic example is an n-form alpha in the open unit ball in R^n. Since alpha is a top-dimensional ...

In an exterior algebra ^ V, a top-dimensional form has degree n where n=dimV. Any form of higher degree must be zero. For example, if V=R^4 then alpha=e_1 ^ e_2 ^ e_3 ^ e_4 ...

A function f is said to be an entire modular form of weight k if it satisfies 1. f is analytic in the upper half-plane H, 2. f((atau+b)/(ctau+d))=(ctau+d)^kf(tau) whenever [a ...

A linear real-valued function omega^1 of vectors v such that omega^1(v)|->R. Vectors (i.e., contravariant vectors or "kets" |psi>) and one-forms (i.e., covariant vectors or ...