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A general quintic equation a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0=0 (1) can be reduced to one of the form y^5+b_2y^2+b_1y+b_0=0, (2) called the principal quintic form. Vieta's ...

A principal nth root omega of unity is a root satisfying the equations omega^n=1 and sum_(i=0)^(n-1)omega^(ij)=0 for j=1, 2, ..., n. Therefore, every primitive root of unity ...

A polyhedron having two polygons in parallel planes as bases and triangular or trapezoidal lateral faces with one side lying in one base and the opposite polyhedron vertex or ...

Given n metric spaces X_1,X_2,...,X_n, with metrics g_1,g_2,...,g_n respectively, the product metric g_1×g_2×...×g_n is a metric on the Cartesian product X_1×X_2×...×X_n ...

A projective space is a space that is invariant under the group G of all general linear homogeneous transformation in the space concerned, but not under all the ...

The projective special orthogonal group PSO_n(q) is the group obtained from the special orthogonal group SO_n(q) on factoring by the scalar matrices contained in that group. ...

Proper covers are defined as covers of a set X which do not contain the entire set X itself as a subset (Macula 1994). Of the five covers of {1,2}, namely {{1},{2}}, {{1,2}}, ...

Any ideal of a ring which is strictly smaller than the whole ring. For example, 2Z is a proper ideal of the ring of integers Z, since 1 not in 2Z. The ideal <X> of the ...

A pseudoinverse is a matrix inverse-like object that may be defined for a complex matrix, even if it is not necessarily square. For any given complex matrix, it is possible ...

A quadratic equation is a second-order polynomial equation in a single variable x ax^2+bx+c=0, (1) with a!=0. Because it is a second-order polynomial equation, the ...