tangent space

The dual basis for the tangent space T is e.

This identity is used in describing the tangent space of certain matrix Lie groups.

These points generate a tangent space of definite dimension "at" each point.

Every point in an analytic space has a tangent space.

There is an associated notion of the tangent space of a measure.

Linear local tangent space alignment and application to face recognition.

It is one half of the value obtained without regard for the tangent space orientation, but with opposite sign.

The general definition is that singular points of C are the cases when the tangent space has dimension 2.

The Fisher information metric is then an inner product on the tangent space.

In other words, F is an asymmetric norm on each tangent space.

Pick a point and consider the tangent space .

It can be defined because Lie groups are manifolds, so have tangent spaces at each point.

If the tangent space is n-dimensional, it can be shown that .

In the second case, the tangent space is that line, considered as affine space.

Tangent spaces may be defined just as in calculus.

At each point of M, this is a linear transformation from one tangent space to another:

Each point of an n-dimensional differentiable manifold has a tangent space.

A scalar is annihilated by the entire tangent space, and so these structures are of type 0.

They are defined as inner products on the tangent space with an appropriate differentiability requirement.

However even if exp is defined on the whole tangent space, it will in general not be a global diffeomorphism.

In particular, one studies the wavefunctions in a tangent space known as a principal bundle.

Smooth vector field on a differentiable manifold, see the tangent space.

A more subtle but no less important feature is that they are imposed eventwise, at the level of tangent spaces.

The infinitesimal increments are then identified with vectors in the tangent space at a point.

Its dual (as a k-vector space) is called tangent space of R.