Search Results for ""

The term Mandelbrot set is used to refer both to a general class of fractal sets and to a particular instance of such a set. In general, a Mandelbrot set marks the set of ...

The principal value of an analytic multivalued function is the single value chosen by convention to be returned for a given argument. Complex multivalued functions have ...

A real normed algebra, also called a composition algebra, is a multiplication * on R^n that respects the length of vectors, i.e., |x*y|=|x|*|y| for x,y in R^n. The only real ...

The reciprocal of a real or complex number z!=0 is its multiplicative inverse 1/z=z^(-1), i.e., z to the power -1. The reciprocal of zero is undefined. A plot of the ...

The Riemann theta function is a complex function of g complex variables that occurs in the construction of quasi-periodic solutions of various equations in mathematical ...

The turning of an object or coordinate system by an angle about a fixed point. A rotation is an orientation-preserving orthogonal transformation. Euler's rotation theorem ...

Let A=a_(ij) be an n×n matrix with complex (or real) entries and eigenvalues lambda_1, lambda_2, ..., lambda_n, then sum_(i=1)^n|lambda_i|^2<=sum_(i,j=1)^n|a_(ij)|^2 (1) ...

The Siegel theta function is a Gamma_n-invariant meromorphic function on the space of all p×p symmetric complex matrices Z=X+iY with positive definite imaginary part. It is ...

Trigonometric functions of npi/7 for n an integer cannot be expressed in terms of sums, products, and finite root extractions on real rational numbers because 7 is not a ...

The d-analog of a complex number s is defined as [s]_d=1-(2^d)/(s^d) (1) (Flajolet et al. 1995). For integer n, [2]!=1 and [n]_d! = [3][4]...[n] (2) = ...