Regular - Definition and Overview

In ordinary English, regular is an adjective or noun used to mean in accordance with the usual customs, conventions, or rules, or frequent, periodic, or symmetric.

The term regular also refers to:

• In the military, a regular unit is a military unit that is part of the regular forces (not militia or reserve). For example, the US 101st Airborne Division is a regular unit, while the 1st US Army (Reserve) is not.

Mathematical meanings include:

• In geometry, a geometric figure is regular if it is symmetric. See regular polygon or regular polyhedron.
• In linear algebra, a regular matrix is an invertible matrix.
• In graph theory, a regular graph is a graph such that the all the degrees of the vertices are equal.
• In computer science, particularly formal language theory, a language is regular if it can be represented by a regular expression.
• In topology, a regular space is one in which points are closed and any point can be separated from any closed set by open sets.
• In algebraic geometry, a function is regular on a variety if for every point there exists an open neighborhood so that the function restricts to a rational function in that neighborhood