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A subset {v_1,...,v_k} of a vector space V, with the inner product <,>, is called orthonormal if <v_i,v_j>=0 when i!=j. That is, the vectors are mutually perpendicular. ...

Hadamard matrices H_n can be constructed using finite field GF(p^m) when p=4l-1 and m is odd. Pick a representation r relatively prime to p. Then by coloring white ...

The term "parameter" is used in a number of ways in mathematics. In general, mathematical functions may have a number of arguments. Arguments that are typically varied when ...

A process of successively crossing out members of a list according to a set of rules such that only some remain. The best known sieve is the sieve of Eratosthenes for ...

For every even dimension 2n, the symplectic group Sp(2n) is the group of 2n×2n matrices which preserve a nondegenerate antisymmetric bilinear form omega, i.e., a symplectic ...

A hyperboloid is a quadratic surface which may be one- or two-sheeted. The two-sheeted hyperboloid is a surface of revolution obtained by rotating a hyperbola about the line ...

A variable is a symbol on whose value a function, polynomial, etc., depends. For example, the variables in the function f(x,y) are x and y. A function having a single ...

In two dimensions, there are two periodic circle packings for identical circles: square lattice and hexagonal lattice. In 1940, Fejes Tóth proved that the hexagonal lattice ...

The Thue-Morse sequence, also called the Morse-Thue sequence or Prouhet-Thue-Morse sequence (Allouche and Cosnard 2000), is one of a number of related sequences of numbers ...

The binomial coefficient (n; k) is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. The symbols ...