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Simplemindedly, a number theoretic transform is a generalization of a fast Fourier transform obtained by replacing e^(-2piik/N) with an nth primitive root of unity. This ...

The eighth proposition in the third book of the Elements is one of Euclid's most complex propositions. It shows that a segment through an outside point D and a circle is ...

A qubit (or quantum bit) is the analog of a bit for quantum computation. Unlike an ordinary bit, which may only assume two possible values (usually called 0 and 1), a qubit ...

A power series sum^(infty)c_kx^k will converge only for certain values of x. For instance, sum_(k=0)^(infty)x^k converges for -1<x<1. In general, there is always an interval ...

Resolution is a widely used word with many different meanings. It can refer to resolution of equations, resolution of singularities (in algebraic geometry), resolution of ...

The Schur decomposition of a complex square matrix A is a matrix decomposition of the form Q^(H)AQ=T=D+N, (1) where Q is a unitary matrix, Q^(H) is its conjugate transpose, ...

Let (x_1,x_2) and (y_1,y_2,y_3) be two sets of complex numbers linearly independent over the rationals. Then at least one of ...

In three dimensions, a parallelepiped is a prism whose faces are all parallelograms. Let A, B, and C be the basis vectors defining a three-dimensional parallelepiped. Then ...

A T_1-space is a topological space fulfilling the T1-separation axiom: For any two points x,y in X there exists two open sets U and V such that x in U and y not in U, and y ...

Let X=(X,tau) be a topological vector space whose continuous dual X^* may or may not separate points (i.e., may or may not be T2). The weak-* (pronounced "weak star") ...