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Given two groups G and H, there are several ways to form a new group. The simplest is the direct product, denoted G×H. As a set, the group direct product is the Cartesian ...

A (presumably autobiographical) character in one of astrophysicist Fred Hoyle's novels opined the following. "I figure that if to be totally known and totally loved is worth ...

For an n×n matrix, let S denote any permutation e_1, e_2, ..., e_n of the set of numbers 1, 2, ..., n, and let chi^((lambda))(S) be the character of the symmetric group ...

Linkages are linked (or constrained) mechanical structures such as those used in robots, excavators, engines, etc. They are also extensively used for character animation in ...

A macron is a bar placed over a single symbol or character, such as x^_. The symbol z^_ is sometimes used to denote the following operations: 1. The complex conjugate z^_. 2. ...

Symbols used to identify irreducible representations of groups: A= singly degenerate state which is symmetric with respect to rotation about the principal C_n axis, B= singly ...

Plancherel's theorem states that the integral of the squared modulus of a function is equal to the integral of the squared modulus of its spectrum. It corresponds to ...

A point group is a group of symmetry operations which all leave at least one point unmoved. Although an isolated object may have an arbitrary Schönflies symbol, the ...

Let chi be a nonprincipal number theoretic character over Z/Zn. Then for any integer h, |sum_(x=1)^hchi(x)|<=2sqrt(n)lnn.

The special unitary group SU_n(q) is the set of n×n unitary matrices with determinant +1 (having n^2-1 independent parameters). SU(2) is homeomorphic with the orthogonal ...