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A real polynomial P is said to be stable if all its roots lie in the left half-plane. The term "stable" is used to describe such a polynomial because, in the theory of linear ...

A generic word for a very large number. The term has no well-defined mathematical meaning. Conway and Guy (1996) define the nth zillion as 10^(3n+3) in the American system ...

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 ...

A transition function describes the difference in the way an object is described in two separate, overlapping coordinate charts, where the description of the same set may ...

Every smooth manifold M has a tangent bundle TM, which consists of the tangent space TM_p at all points p in M. Since a tangent space TM_p is the set of all tangent vectors ...

A conformal mapping, also called a conformal map, conformal transformation, angle-preserving transformation, or biholomorphic map, is a transformation w=f(z) that preserves ...

Roughly speaking, the metric tensor g_(ij) is a function which tells how to compute the distance between any two points in a given space. Its components can be viewed as ...

The Euclidean plane parametrized by coordinates, so that each point is located based on its position with respect to two perpendicular lines, called coordinate axes. They are ...

The tangent space at a point p in an abstract manifold M can be described without the use of embeddings or coordinate charts. The elements of the tangent space are called ...

An automorphism is an isomorphism of a system of objects onto itself. The term derives from the Greek prefix alphaupsilontauomicron (auto) "self" and ...