Mathematical degeneracy - Definition

In mathematics, a degenerate case is a limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class.

• A point is a degenerate case of a circle, namely one with radius 0. The circle is a degenerate form of an ellipse, namely one with eccentricity 0.
• The line is a degenerate form of a parabola if the parabola resides on a tangent plane.
• A hyperbola can degenerate into two lines crossing at a point, through a family of hyperbolas having those lines as common asymptotes.
• See "general position" for other examples.

Another usage of the word comes in eigenproblems: a degenerate eigenvalue is one that has more than one linearly independent eigenvector.

See also: degeneracy, trivial.