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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" ...

A ring without zero divisors in which an integer norm and an associated division algorithm (i.e., a Euclidean algorithm) can be defined. For signed integers, the usual norm ...

The exsecant is a little-used trigonometric function defined by exsec(x)=secx-1, (1) where secx is the secant. The exsecant can be extended to the complex plane as ...

The Heisenberg group H^n in n complex variables is the group of all (z,t) with z in C^n and t in R having multiplication (w,t)(z,t^')=(w+z,t+t^'+I[w^*z]) (1) where w^* is the ...

The L^2-inner product of two real functions f and g on a measure space X with respect to the measure mu is given by <f,g>_(L^2)=int_Xfgdmu, sometimes also called the bracket ...

A horizontal line placed above multiple quantities to indicate that they form a unit. It is most commonly used to denote 1. A radical (sqrt(12345)), 2. Repeating decimals ...

A closed subspace of a Banach space X is called weakly complemented if the dual i^* of the natural embedding i:M↪X has a right inverse as a bounded operator. For example, the ...

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 ...

Informally, an elliptic curve is a type of cubic curve whose solutions are confined to a region of space that is topologically equivalent to a torus. The Weierstrass elliptic ...

A fractal which can be constructed using string rewriting beginning with a cell [1] and iterating the rules {0->[0 1 0; 1 1 1; 0 1 0],1->[1 1 1; 1 1 1; 1 1 1]}. (1) The size ...