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The term normal form is used in a variety of contexts. Many of the uses in mathematics are special cases of a single situation, looked at abstractly: within an equivalence class one specifies a representative element, which is in a simplest or most manageable or otherwise tidiest and most desirable form, in terms of structure or syntax. A little more loosely, an equivalence class might contain several examples of such special, distinguished elements. For example, the Jordan normal form under similarity of matrices (link below) may mean any suitable block matrix in similarity class, and in the general case there can be several such.

In classical logic, propositions may be in:

• Negation normal form
• Conjunctive normal form
• Disjunctive normal form
• Algebraic normal form

In formal language theory:

• Chomsky normal form
• Greibach normal form
• Kuroda normal form

In relational databaseA relational database is a database based on the relational model. Strictly speaking, this means a relational database takes the form of a specific collection of data. The database software that is used to manage the data is called a relational database m theory

• first normal form
• second normal form
• third normal form
• fourth normal form

see database normalizationDatabase normalization is a series of steps followed to obtain a database design that allows for consistent storage and efficient access of data in a relational database. These steps reduce data redundancy and the risk of data becoming inconsistent. Howev for all four.

In linear algebraLinear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (or linear spaces), linear transformations, and systems of linear equations. Vector spaces are a central theme in modern mathematics; thus, linear algebra is wi:

• Jordan normal formIn linear algebra, the Jordan normal form also called the Jordan canonical form named in honor of the 19th and early 20th-century French mathematician Camille Jordan, answers the question, for a given square matrix M over a field K to what extent M can be
• Frobenius normal formLinear algebra Matrix normal forms In linear algebra, the Frobenius normal form of a matrix is a normal form that reflects the structure of the minimal polynomial of a matrix. The idea of the companion matrix of a polynomial demonstrates this relationship

In proof theoryLogic Proof theory Proof theory studied as a branch of mathematical logic, represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures, suc

• Normal formAn inference of natural deduction is a normal form according to Dag Prawitz, if no formula occurrence is both the principal premise of an elimination rule and the conclusion of an introduction rule. for proofs in natural deductionIn mathematical logic, natural deduction is the name given to a class of foundational approaches for two key concepts in logic, propositions and proofs. There is no universal agreement on the proper foundation of these concepts; natural deduction takes th

In the lambda calculus

• Beta normal form and Beta-eta normal form

In musical set theory:

• the normal form of a pitch or pitch class set, which is the order that occupies the smallest possible span and is stacked leftmost.

To transform something into a normal form is often called normalization.

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Topics: Normal Form Class Theory Database Normalization Jordan Pitch...

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Normal distributionProbability density function of Gaussian distribution (bell curve). The normal distribution is an extremely important probability distribution in many fields. It is also called the Gaussian distribution especially in physics and engineering. It is actuall Normal subgroupIn mathematics, a normal subgroup ''N of a group G is a subgroup invariant under conjugation; that is, for each element n in N and each g in G the element g-1ng is still in N''. The statement N is a normal subgroup of G is written: :. Another way to put t Normalized frequencyIn telecommunication, the term normalized frequency ( V ) has several meanings; it may refer to the ratio between an actual frequency and a reference value, or to the ratio between an actual frequency and its nominal value. In an optical fiber, normalized Normal spaceIn topology and related branches of mathematics, normal spaces T spaces and T spaces are particularly nice kinds of topological spaces. These conditions are examples of separation axioms. Definitions Suppose that X is a topological space. X is a normal sp Normal, IllinoisNormal is a town located in McLean County, Illinois. As of the 2000 census, the town had a total population of 45,386. The town, originally known as North Bloomington, took its name from the Illinois Normal College located there, an old name for a college Normal morphismIn category theory and its applications to mathematics, a normal monomorphism or normal epimorphism is a particularly well-behaved type of morphism. A normal category is a category in which morphisms are normal, whenever reasonable. Definition A category Normal Normal vector Normal matrix Normal science Normal lens Normal operator Normal form Normal number Normal goods