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The identities between the symmetric polynomials Pi_k(x_1,...,x_n) and the sums of kth powers of their variables S_k(x_1,...,x_n)=sum_(j=1)^nx_j^k. (1) The identities are ...

There are two equivalent definitions for a nilpotent matrix. 1. A square matrix whose eigenvalues are all 0. 2. A square matrix A such that A^n is the zero matrix 0 for some ...

Let S_N(s)=sum_(n=1)^infty[(n^(1/N))]^(-s), (1) where [x] denotes nearest integer function, i.e., the integer closest to x. For s>3, S_2(s) = 2zeta(s-1) (2) S_3(s) = ...

A group or other algebraic object is called non-Abelian if the law of commutativity does not always hold, i.e., if the object is not Abelian. For example, the group of ...

A normal extension is the splitting field for a collection of polynomials. In the case of a finite algebraic extension, only one polynomial is necessary.

There are a number of attractive polyhedron compounds consisting of nine octahedra. The compound illustrated above can be constructed as the dual of cube 9-compound. The ...

An octic curve is an algebraic curve of order eight. The pear curve is an example of an octic curve.

An important result in ergodic theory. It states that any two "Bernoulli schemes" with the same measure-theoretic entropy are measure-theoretically isomorphic.

Given a pair of orthologic triangles, the point where the perpendiculars from the vertices of the first to the sides of the second concur and the point where the ...

A Pareto plot is type of plot used in quality control applications that combines a bar chart displaying percentages of categories in the data with a line graph showing ...