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There are several meanings of "null vector" in mathematics. 1. The most common meaning of null vector is the n-dimensional vector 0 of length 0. i.e., the vector with n ...

An orthogonal transformation is a linear transformation T:V->V which preserves a symmetric inner product. In particular, an orthogonal transformation (technically, an ...

The surface of revolution of the parabola which is the shape used in the reflectors of automobile headlights (Steinhaus 1999, p. 242; Hilbert and Cohn-Vossen 1999). It is a ...

A number which is simultaneously a pentagonal number P_n and triangular number T_m. Such numbers exist when 1/2n(3n-1)=1/2m(m+1). (1) Completing the square gives ...

In Euclidean space R^3, the curve that minimizes the distance between two points is clearly a straight line segment. This can be shown mathematically as follows using ...

The word residue is used in a number of different contexts in mathematics. Two of the most common uses are the complex residue of a pole, and the remainder of a congruence. ...

The study of manifolds having a complete Riemannian metric. Riemannian geometry is a general space based on the line element ds=F(x^1,...,x^n;dx^1,...,dx^n), with F(x,y)>0 ...

For a set of n numbers or values of a discrete distribution x_i, ..., x_n, the root-mean-square (abbreviated "RMS" and sometimes called the quadratic mean), is the square ...

The p×p square matrix formed by setting s_(ij)=xi^(ij), where xi is a pth root of unity. The Schur matrix has a particularly simple determinant given by ...

The general sextic equation x^6+a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0=0 can be solved in terms of Kampé de Fériet functions, and a restricted class of sextics can be solved in ...