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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 ...

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 ...

An antisymmetric matrix, also known as a skew-symmetric or antimetric matrix, is a square matrix that satisfies the identity A=-A^(T) (1) where A^(T) is the matrix transpose. ...

A real normed algebra, also called a composition algebra, is a multiplication * on R^n that respects the length of vectors, i.e., |x*y|=|x|*|y| for x,y in R^n. The only real ...

A solvable Lie group is a Lie group G which is connected and whose Lie algebra g is a solvable Lie algebra. That is, the Lie algebra commutator series ...

A group G is said to act on a set X when there is a map phi:G×X->X such that the following conditions hold for all elements x in X. 1. phi(e,x)=x where e is the identity ...

A group G is a finite or infinite set of elements together with a binary operation (called the group operation) that together satisfy the four fundamental properties of ...

Eigenvectors are a special set of vectors associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic vectors, ...

In general, there are two important types of curvature: extrinsic curvature and intrinsic curvature. The extrinsic curvature of curves in two- and three-space was the first ...

Cylindrical coordinates are a generalization of two-dimensional polar coordinates to three dimensions by superposing a height (z) axis. Unfortunately, there are a number of ...