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The single bar | is a notation variously used to denote the absolute value |x|, complex modulus |z|, vector norm |x|, determinant |A|, or "divides" (a|b).

A horizontal line placed under a symbol to indicate some special property. Underscores are sometimes used instead of over-arrows or bold typeface to indicate a vector, for ...

The nullity of a linear transformation f:V->W of vector spaces is the dimension of its null space. The nullity and the map rank add up to the dimension of V, a result ...

A fundamental result of de Rham cohomology is that the kth de Rham cohomology vector space of a manifold M is canonically isomorphic to the Alexander-Spanier cohomology ...

An anchor is the bundle map rho from a vector bundle A to the tangent bundle TB satisfying 1. [rho(X),rho(Y)]=rho([X,Y]) and 2. [X,phiY]=phi[X,Y]+(rho(X)·phi)Y, where X and Y ...

A notation invented by Dirac which is very useful in quantum mechanics. The notation defines the "ket" vector, denoted |psi>, and its conjugate transpose, called the "bra" ...

An inner product is a generalization of the dot product. In a vector space, it is a way to multiply vectors together, with the result of this multiplication being a scalar. ...

Newton's method for finding roots of a complex polynomial f entails iterating the function z-[f(z)/f^'(z)], which can be viewed as applying the Euler backward method with ...

A game in which the possible moves are the same for each player in any position. All positions in all impartial games form an additive Abelian group. For impartial games in ...

alpha(x) = 1/(sqrt(2pi))int_(-x)^xe^(-t^2/2)dt (1) = sqrt(2/pi)int_0^xe^(-t^2/2)dt (2) = 2Phi(x) (3) = erf(x/(sqrt(2))), (4) where Phi(x) is the normal distribution function ...