Search Results for ""

A unit vector is a vector of length 1, sometimes also called a direction vector (Jeffreys and Jeffreys 1988). The unit vector v^^ having the same direction as a given ...

From the point of view of coordinate charts, the notion of tangent space is quite simple. The tangent space consists of all directions, or velocities, a particle can take. In ...

The tangent plane to a surface at a point p is the tangent space at p (after translating to the origin). The elements of the tangent space are called tangent vectors, and ...

The vector space generated by the rows of a matrix viewed as vectors. The row space of a n×m matrix A with real entries is a subspace generated by n elements of R^m, hence ...

The squared norm of a four-vector a=(a_0,a_1,a_2,a_3)=a_0+a is given by the dot product a^2=a_mua^mu=(a^0)^2-a·a, (1) where a·a is the usual vector dot product in Euclidean ...

Euclidean n-space, sometimes called Cartesian space or simply n-space, is the space of all n-tuples of real numbers, (x_1, x_2, ..., x_n). Such n-tuples are sometimes called ...

Lorentzian n-space is the inner product space consisting of the vector space R^n together with the n-dimensional Lorentzian inner product. In the event that the (1,n-1) ...

A Fréchet space is a complete and metrizable space, sometimes also with the restriction that the space be locally convex. The topology of a Fréchet space is defined by a ...

There are at least two distinct notions of linear space throughout mathematics. The term linear space is most commonly used within functional analysis as a synonym of the ...

Let x be a point in an n-dimensional compact manifold M, and attach at x a copy of R^n tangential to M. The resulting structure is called the tangent space of M at x and is ...