Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Degeneracy_(mathematics)> ?p ?o }
- Degeneracy_(mathematics) abstract "In mathematics, a degenerate case is a limiting case in which an element of a class of objects is qualitatively different from the rest of the class and hence belongs to another, usually simpler, class. Degeneracy is the condition of being a degenerate case.The definitions of many classes of composite or structured objects include (often implicitly) inequalities. For example, the angles and the side lengths of a triangle are supposed to be positive. The limiting cases, where one of these elements of the triangle is zero, are degenerate triangles.Often, the degenerate cases are the exceptional cases where changes to the usual dimension or the cardinality of the object (or of some part of it) occur. For example, a triangle is an object of dimension two, and a degenerate triangle is contained in a line, and its dimension is thus one. Similarly, the solution set of a system of equations that depends on parameters generally has a fixed cardinality and dimension, but cardinality and/or dimension may be different for some exceptional values, called degenerate cases. In such a degenerate case, the solution set is said to be degenerate.For some classes of composite objects, the degenerate cases depend on the properties that are specifically studied. In particular, the class of objects may often be defined or characterized by systems of equations. Commonly, a given class of objects may be defined by several different systems of equations, and these different systems of equations may lead to different degenerate cases, while characterizing the same non-degenerate cases. This may be the reason for which there is no general definition of degeneracy, although the concept is widely used, and defined, if needed, in each specific situation.A degenerate case thus has special features, which makes it non-generic. However not all non-generic cases are degenerate. For example, right triangles, isosceles triangles and equilateral triangles are non-generic and non-degenerate. Frequently, degenerate cases correspond to singularities either in the object or in some configuration space. For example, a conic section is degenerate if and only if it has singular points.".
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- Degeneracy_(mathematics) wikiPageRevisionID "707022513".
- Degeneracy_(mathematics) wikiPageWikiLink Algebraic_equation.
- Degeneracy_(mathematics) wikiPageWikiLink Angle.
- Degeneracy_(mathematics) wikiPageWikiLink Asymptote.
- Degeneracy_(mathematics) wikiPageWikiLink Cardinality.
- Degeneracy_(mathematics) wikiPageWikiLink Category:Mathematical_concepts.
- Degeneracy_(mathematics) wikiPageWikiLink Characteristic_polynomial.
- Degeneracy_(mathematics) wikiPageWikiLink Circle.
- Degeneracy_(mathematics) wikiPageWikiLink Collinearity.
- Degeneracy_(mathematics) wikiPageWikiLink Configuration_space.
- Degeneracy_(mathematics) wikiPageWikiLink Conic_section.
- Degeneracy_(mathematics) wikiPageWikiLink Convex_polygon.
- Degeneracy_(mathematics) wikiPageWikiLink Convex_polytope.
- Degeneracy_(mathematics) wikiPageWikiLink Coplanarity.
- Degeneracy_(mathematics) wikiPageWikiLink Degeneracy_(graph_theory).
- Degeneracy_(mathematics) wikiPageWikiLink Degenerate_bilinear_form.
- Degeneracy_(mathematics) wikiPageWikiLink Degenerate_distribution.
- Degeneracy_(mathematics) wikiPageWikiLink Degenerate_energy_levels.
- Degeneracy_(mathematics) wikiPageWikiLink Digon.
- Degeneracy_(mathematics) wikiPageWikiLink Dimension.
- Degeneracy_(mathematics) wikiPageWikiLink Dirac_delta_function.
- Degeneracy_(mathematics) wikiPageWikiLink Eccentricity_(mathematics).
- Degeneracy_(mathematics) wikiPageWikiLink Eigenvalues_and_eigenvectors.
- Degeneracy_(mathematics) wikiPageWikiLink Ellipse.
- Degeneracy_(mathematics) wikiPageWikiLink Equilateral_triangle.
- Degeneracy_(mathematics) wikiPageWikiLink Focus_(geometry).
- Degeneracy_(mathematics) wikiPageWikiLink General_position.
- Degeneracy_(mathematics) wikiPageWikiLink Generic_property.
- Degeneracy_(mathematics) wikiPageWikiLink Graph_(discrete_mathematics).
- Degeneracy_(mathematics) wikiPageWikiLink Hamiltonian_(quantum_mechanics).
- Degeneracy_(mathematics) wikiPageWikiLink Hyperbola.
- Degeneracy_(mathematics) wikiPageWikiLink Inversive_geometry.
- Degeneracy_(mathematics) wikiPageWikiLink Irreducible_component.
- Degeneracy_(mathematics) wikiPageWikiLink Isosceles_triangle.
- Degeneracy_(mathematics) wikiPageWikiLink Limiting_case_(mathematics).
- Degeneracy_(mathematics) wikiPageWikiLink Line_(geometry).
- Degeneracy_(mathematics) wikiPageWikiLink Line_segment.
- Degeneracy_(mathematics) wikiPageWikiLink Linear_continuum.
- Degeneracy_(mathematics) wikiPageWikiLink Mathematical_object.
- Degeneracy_(mathematics) wikiPageWikiLink Mathematics.
- Degeneracy_(mathematics) wikiPageWikiLink Monogon.
- Degeneracy_(mathematics) wikiPageWikiLink Multiplicity_(mathematics).
- Degeneracy_(mathematics) wikiPageWikiLink Parabola.
- Degeneracy_(mathematics) wikiPageWikiLink Parameter.
- Degeneracy_(mathematics) wikiPageWikiLink Pathological_(mathematics).
- Degeneracy_(mathematics) wikiPageWikiLink Plane_(geometry).
- Degeneracy_(mathematics) wikiPageWikiLink Plane_curve.
- Degeneracy_(mathematics) wikiPageWikiLink Point_(geometry).
- Degeneracy_(mathematics) wikiPageWikiLink Polygon.
- Degeneracy_(mathematics) wikiPageWikiLink Polynomial.
- Degeneracy_(mathematics) wikiPageWikiLink Quantum_mechanics.
- Degeneracy_(mathematics) wikiPageWikiLink Random_variable.
- Degeneracy_(mathematics) wikiPageWikiLink Rectangle.
- Degeneracy_(mathematics) wikiPageWikiLink Right_triangle.
- Degeneracy_(mathematics) wikiPageWikiLink Semi-minor_axis.
- Degeneracy_(mathematics) wikiPageWikiLink Simultaneous_equations.
- Degeneracy_(mathematics) wikiPageWikiLink Singularity_theory.
- Degeneracy_(mathematics) wikiPageWikiLink Solution_set.
- Degeneracy_(mathematics) wikiPageWikiLink Sphere.
- Degeneracy_(mathematics) wikiPageWikiLink Symmetry.
- Degeneracy_(mathematics) wikiPageWikiLink Tangent_space.
- Degeneracy_(mathematics) wikiPageWikiLink Tetrahedron.
- Degeneracy_(mathematics) wikiPageWikiLink Torus.
- Degeneracy_(mathematics) wikiPageWikiLink Triangle.
- Degeneracy_(mathematics) wikiPageWikiLink Triviality_(mathematics).
- Degeneracy_(mathematics) wikiPageWikiLink Vacuous_truth.
- Degeneracy_(mathematics) wikiPageWikiLink Vertex_(geometry).
- Degeneracy_(mathematics) wikiPageWikiLink Volume.
- Degeneracy_(mathematics) wikiPageWikiLink Zero_of_a_function.
- Degeneracy_(mathematics) wikiPageWikiLinkText "Degeneracy (mathematics)".
- Degeneracy_(mathematics) wikiPageWikiLinkText "Degeneracy (mathematics)#Elsewhere".
- Degeneracy_(mathematics) wikiPageWikiLinkText "Degeneracy".
- Degeneracy_(mathematics) wikiPageWikiLinkText "Degeneracy_(mathematics)".
- Degeneracy_(mathematics) wikiPageWikiLinkText "Non-degeneracy".
- Degeneracy_(mathematics) wikiPageWikiLinkText "degeneracies".
- Degeneracy_(mathematics) wikiPageWikiLinkText "degeneracy (mathematics)".
- Degeneracy_(mathematics) wikiPageWikiLinkText "degeneracy of solutions".
- Degeneracy_(mathematics) wikiPageWikiLinkText "degeneracy".
- Degeneracy_(mathematics) wikiPageWikiLinkText "degenerate case".
- Degeneracy_(mathematics) wikiPageWikiLinkText "degenerate examples".
- Degeneracy_(mathematics) wikiPageWikiLinkText "degenerate".
- Degeneracy_(mathematics) wikiPageWikiLinkText "degenerates".
- Degeneracy_(mathematics) wikiPageWikiLinkText "degenerating".
- Degeneracy_(mathematics) wikiPageWikiLinkText "degeneration".
- Degeneracy_(mathematics) wikiPageWikiLinkText "non-degeneracy".
- Degeneracy_(mathematics) wikiPageWikiLinkText "non-degenerate".
- Degeneracy_(mathematics) wikiPageWikiLinkText "nondegenerate".
- Degeneracy_(mathematics) id "Degenerate".
- Degeneracy_(mathematics) title "Degenerate".
- Degeneracy_(mathematics) wikiPageUsesTemplate Template:About.
- Degeneracy_(mathematics) wikiPageUsesTemplate Template:Main.
- Degeneracy_(mathematics) wikiPageUsesTemplate Template:MathWorld.
- Degeneracy_(mathematics) wikiPageUsesTemplate Template:Unreferenced.
- Degeneracy_(mathematics) subject Category:Mathematical_concepts.
- Degeneracy_(mathematics) hypernym Case.
- Degeneracy_(mathematics) type SupremeCourtOfTheUnitedStatesCase.