Search Results for ""

A basis vector in an n-dimensional vector space is one of any chosen set of n vectors in the space forming a vector basis, i.e., having the property that every vector in the ...

The magnitude (length) of a vector x=(x_1,x_2,...,x_n) is given by |x|=sqrt(x_1^2+x_2^2+...+x_n^2).

An ordered vector basisv_1,...,v_n for a finite-dimensional vector space V defines an orientation. Another basis w_i=Av_i gives the same orientation if the matrix A has a ...

K=(dT)/(ds), where T is the tangent vector defined by T=((dx)/(ds))/(|(dx)/(ds)|).

The vector r from the origin to the current position. It is also called the position vector. The derivative of r satisfies ...

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 real vector space is a vector space whose field of scalars is the field of reals. A linear transformation between real vector spaces is given by a matrix with real entries ...

An abstract vector space of dimension n over a field k is the set of all formal expressions a_1v_1+a_2v_2+...+a_nv_n, (1) where {v_1,v_2,...,v_n} is a given set of n objects ...

Given an n-dimensional vector x=[x_1; x_2; |; x_n], (1) a general vector norm |x|, sometimes written with a double bar as ||x||, is a nonnegative norm defined such that 1. ...

A tangent vector v_(p)=v_1x_u+v_2x_v is a principal vector iff det[v_2^2 -v_1v_2 v_1^2; E F G; e f g]=0, where e, f, and g are coefficients of the first fundamental form and ...