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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 ...

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 ...

The asterisk *, also called a "star," is used for a number of different purposed in mathematics. The most common usage is to denote multiplication so, for example, 2*3=2×3=6. ...

A plane tiling is said to be isohedral if the symmetry group of the tiling acts transitively on the tiles, and n-isohedral if the tiles fall into n orbits under the action of ...

The term folium means "leaf" in Latin and refers and refers to a plane curve having "leaf-shaped" rounded lobes. There are a number of different sorts of folia, including ...

Symmetry operations include the improper rotation, inversion operation, mirror plane, and rotation. Together, these operations create 32 crystal classes corresponding to the ...

Let {a_i}_(i=0)^(N-1) be a periodic sequence, then the autocorrelation of the sequence, sometimes called the periodic autocorrelation (Zwillinger 1995, p. 223), is the ...

The spherical Bessel function of the first kind, denoted j_nu(z), is defined by j_nu(z)=sqrt(pi/(2z))J_(nu+1/2)(z), (1) where J_nu(z) is a Bessel function of the first kind ...

P is the point on the line AB such that PA^_/PB^_=1. It can also be thought of as the point of intersection of two parallel lines. In 1639, Desargues (1864) became the first ...