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The minimal polynomial of an algebraic number zeta is the unique irreducible monic polynomial of smallest degree p(x) with rational coefficients such that p(zeta)=0 and whose ...

The dual vector space to a real vector space V is the vector space of linear functions f:V->R, denoted V^*. In the dual of a complex vector space, the linear functions take ...

A group action G×X->X is called free if, for all x in X, gx=x implies g=I (i.e., only the identity element fixes any x). In other words, G×X->X is free if the map G×X->X×X ...

The contraction of a tensor is obtained by setting unlike indices equal and summing according to the Einstein summation convention. Contraction reduces the tensor rank by 2. ...

The dihedral group D_3 is a particular instance of one of the two distinct abstract groups of group order 6. Unlike the cyclic group C_6 (which is Abelian), D_3 is ...

The operation of multiplication, i.e., a times b. Various notations are a×b, a·b, a*b, ab, and (a)(b). The "multiplication sign" × is based on Saint Andrew's cross (Bergamini ...

A group G is said to act on a set X when there is a map phi:G×X->X such that the following conditions hold for all elements x in X. 1. phi(e,x)=x where e is the identity ...

Consider the Fibonacci-like recurrence a_n=+/-a_(n-1)+/-a_(n-2), (1) where a_0=0, a_1=1, and each sign is chosen independently and at random with probability 1/2. ...

Four circles may be drawn through an arbitrary point P on a torus. The first two circles are obvious: one is in the plane of the torus and the second perpendicular to it. The ...

The Cartesian graph product G=G_1 square G_2, also called the graph box product and sometimes simply known as "the" graph product (Beineke and Wilson 2004, p. 104) and ...