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A permutation, also called an "arrangement number" or "order," is a rearrangement of the elements of an ordered list S into a one-to-one correspondence with S itself. The ...

A permutation cycle is a subset of a permutation whose elements trade places with one another. Permutations cycles are called "orbits" by Comtet (1974, p. 256). For example, ...

An n×n complex matrix A is called positive definite if R[x^*Ax]>0 (1) for all nonzero complex vectors x in C^n, where x^* denotes the conjugate transpose of the vector x. In ...

The biconjugate gradient method often displays rather irregular convergence behavior. Moreover, the implicit LU decomposition of the reduced tridiagonal system may not exist, ...

A random matrix is a matrix of given type and size whose entries consist of random numbers from some specified distribution. Random matrix theory is cited as one of the ...

The (first) rhombic dodecahedron is the dual polyhedron of the cuboctahedron A_1 (Holden 1971, p. 55) and Wenninger dual W_(11). Its sometimes also called the rhomboidal ...

The rhombic hexecontahedron is a 60-faced polyhedron that can be obtained by stellating the rhombic triacontahedron by placing a plane along each edge which is perpendicular ...

A positive integer n is called a base-b Rhonda number if the product of the base-b digits of n is equal to b times the sum of n's prime factors. These numbers were named by ...

A Riemann surface is a surface-like configuration that covers the complex plane with several, and in general infinitely many, "sheets." These sheets can have very complicated ...

Rule 30 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...