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The Euclidean metric is the function d:R^n×R^n->R that assigns to any two vectors in Euclidean n-space x=(x_1,...,x_n) and y=(y_1,...,y_n) the number ...

Given a set V of m vectors (points in R^n), the Gram matrix G is the matrix of all possible inner products of V, i.e., g_(ij)=v_i^(T)v_j. where A^(T) denotes the transpose. ...

The equation defining Killing vectors. L_Xg_(ab)=X_(a;b)+X_(b;a)=2X_((a;b))=0, where L is the Lie derivative and X_(b;a) is a covariant derivative.

A lattice which is built up of layers of n-dimensional lattices in (n+1)-dimensional space. The vectors specifying how layers are stacked are called glue vectors. The order ...

A linear code over a finite field with q elements F_q is a linear subspace C subset F_q^n. The vectors forming the subspace are called codewords. When codewords are chosen ...

The span of subspace generated by vectors v_1 and v_2 in V is Span(v_1,v_2)={rv_1+sv_2:r,s in R}. A set of vectors m={v_1,...,v_n} can be tested to see if they span ...

An additive group is a group where the operation is called addition and is denoted +. In an additive group, the identity element is called zero, and the inverse of the ...

Differential evolution is a stochastic parallel direct search evolution strategy optimization method that is fairly fast and reasonably robust. Differential evolution is ...

A set of vectors in Euclidean n-space is said to satisfy the Haar condition if every set of n vectors is linearly independent (Cheney 1999). Expressed otherwise, each ...

To solve the system of differential equations (dx)/(dt)=Ax(t)+p(t), (1) where A is a matrix and x and p are vectors, first consider the homogeneous case with p=0. The ...