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A number n is called amenable if it can be built up from integers a_1, a_2, ..., a_k by either addition or multiplication such that sum_(i=1)^na_i=product_(i=1)^na_i=n (1) ...

The q-series identity product_(n=1)^(infty)((1-q^(2n))(1-q^(3n))(1-q^(8n))(1-q^(12n)))/((1-q^n)(1-q^(24n))) = ...

The q-analog of pi pi_q can be defined by setting a=0 in the q-factorial [a]_q!=1(1+q)(1+q+q^2)...(1+q+...+q^(a-1)) (1) to obtain ...

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 ...

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 of three elements, also called a triad. A triple is therefore a 3-tuple.

An extension of a group H by a group N is a group G with a normal subgroup M such that M=N and G/M=H. This information can be encoded into a short exact sequence of groups ...

Linear Algebra

Lagrange's identity is the algebraic identity (sum_(k=1)^na_kb_k)^2=(sum_(k=1)^na_k^2)(sum_(k=1)^nb_k^2)-sum_(1<=k<j<=n)(a_kb_j-a_jb_k)^2 (1) (Mitrinović 1970, p. 41; Marsden ...

The lattice method is an alternative to long multiplication for numbers. In this approach, a lattice is first constructed, sized to fit the numbers being multiplied. If we ...