Canonical form

Under a normal form ( also canonical form ) refers to a representation with certain given properties. Sometimes the representation is unique. Formally, a normal form for the last element in a chain of a well-founded relation. The relation is in this case defined by the various allowable transformations, such as is the step shape (see below), a matrix A in relation to a matrix B where B is apparent by Pivoting of A. The soundness of the relations follows from the finiteness of the number of manipulations.

List of normal forms

Important, concrete normal forms are

• In mathematics, a representation of an object that has certain specified properties and can be uniquely determined for all objects of this type. In particular: the Hessian normal form of a plane
• The levels normal form of a system of linear equations, Gaussian elimination method see
• The Jordan canonical form of a square matrix
• The Frobenius normal shape also normal rational form of a square matrix
• The normal form of a linear function, see Linear Function
• The normal form of a quadratic equation, see Quadratic Equation
• The normal form of a quadric, quadric see # Normal Forms

• In game theory a representation form of a game, see normal form ( game theory)
• In theoretical computer science, a simple form of a context-free grammar, see Chomsky hierarchy. in particular the Chomsky normal form
• The Greibach normal form
• The Gentzen - normal form, see Gentz ​​shear Law

• In practical computer science in relational databases, the data structure obtained by gradually removing redundancies, see normalization (database)

• In the logic a representation form of a logical formula, in particular the Shannon - normal form
• The negation normal form
• Formulas standard in the canonical form, in particular as: Conjunctive normal form
• Disjunctive Normal Form
• Ring sum normal form

• In predicate logic the adjusted normal form
• The negation normal form
• The prenex normal form
• The Skolem
• The clause normal form

• In abstract reduction systems, an object that can not be reduced

• In digital technology with digital filters in formal form of the minimum number of its elements, taking into account the desired filter characteristics, see Digital filter

• Mathematical concept