For "canonical form" in linguistics, see Lemma (morphology).
For "canonical form" in Catholic matrimonial law, see Marriage in the Catholic Church § Canonical form.
This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Canonical form" – news · newspapers · books · scholar · JSTOR(December 2007) (Learn how and when to remove this message)
Algorithmic anagram test using multisets as canonical forms: The strings "madam curie" and "radium came" are given as C arrays. Each one is converted into a canonical form by sorting. Since both sorted strings literally agree, the original strings were anagrams of each other.
In mathematics and computer science, a canonical, normal, or standardform of a mathematical object is a standard way of presenting that object as a mathematical expression. Often, it is one which provides the simplest representation of an object and allows it to be identified in a unique way. The distinction between "canonical" and "normal" forms varies from subfield to subfield. In most fields, a canonical form specifies a unique representation for every object, while a normal form simply specifies its form, without the requirement of uniqueness.[1]
The canonical form of a positive integer in decimal representation is a finite sequence of digits that does not begin with zero. More generally, for a class of objects on which an equivalence relation is defined, a canonical form consists in the choice of a specific object in each class. For example:
Jordan normal form is a canonical form for matrix similarity.
The row echelon form is a canonical form, when one considers as equivalent a matrix and its left product by an invertible matrix.
In computer science, and more specifically in computer algebra, when representing mathematical objects in a computer, there are usually many different ways to represent the same object. In this context, a canonical form is a representation such that every object has a unique representation (with canonicalization being the process through which a representation is put into its canonical form).[2] Thus, the equality of two objects can easily be tested by testing the equality of their canonical forms.
Despite this advantage, canonical forms frequently depend on arbitrary choices (like ordering the variables), which introduce difficulties for testing the equality of two objects resulting on independent computations. Therefore, in computer algebra, normal form is a weaker notion: A normal form is a representation such that zero is uniquely represented. This allows testing for equality by putting the difference of two objects in normal form.
Canonical form can also mean a differential form that is defined in a natural (canonical) way.
^In some occasions, the term "canonical" and "normal" can also be used interchangeably, as in Jordan canonical form and Jordan normal form (see Jordan normal form on MathWorks).
^The term 'canonization' is sometimes incorrectly used for this.
In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical...
canonical disjunctive normal form (CDNF) or minterm canonicalform, and its dual, the canonical conjunctive normal form (CCNF) or maxterm canonical form...
algebra, a Jordan normal form, also known as a Jordan canonicalform (JCF), is an upper triangular matrix of a particular form called a Jordan matrix representing...
literature in that context. In mathematics, canonical example is often used to mean 'archetype'. Canonicalform, a natural unique representation of an object...
more than one possible representation into a "standard", "normal", or canonicalform. This can be done to compare different representations for equivalence...
reduced row echelon form or in canonicalform if its augmented matrix is in reduced row echelon form. The canonicalform may be viewed as an explicit solution...
algebra, the Frobenius normal form or rational canonicalform of a square matrix A with entries in a field F is a canonicalform for matrices obtained by conjugation...
f is in Blake canonicalform (BCF), also called the complete sum of prime implicants, the complete sum, or the disjunctive prime form, when it is a disjunction...
alternative sequences are in general canonically equivalent. The rules that define their sequencing in the canonicalform also define whether they are considered...
In mathematics, in linear algebra, a Weyr canonicalform (or, Weyr form or Weyr matrix) is a square matrix which (in some sense) induces "nice" properties...
called the canonicalform of the rational number. Starting from a rational number a b , {\displaystyle {\tfrac {a}{b}},} its canonicalform may be obtained...
controllability is still analogous. Nonlinear systems in the control-affine form x ˙ = f ( x ) + ∑ i = 1 m g i ( x ) u i {\displaystyle {\dot {\mathbf {x}...
just a constant value (a resistance) remains. The Brune synthesis is canonical, that is, the number of elements in the final synthesised network is equal...
generalization of one of these equations, as it can always be put into the canonicalform u x x + u y y + (lower-order terms) = 0 {\displaystyle u_{xx}+u_{yy}+{\text{...
0 {\displaystyle Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0\,} can be converted to canonicalform in transformed variables x ~ , y ~ {\displaystyle {\tilde {x}},{\tilde...
efficient. The simplex algorithm operates on linear programs in the canonicalform maximize c T x {\textstyle \mathbf {c^{T}} \mathbf {x} } subject to...
indeed invalid due to the lack of form. However, in situations where there was a complete absence of the canonicalform (e.g. if the marriage was concluded...
the canonicalform a requirement even where the decree of the Council of Trent had not been promulgated. While allowing for exceptions, the canonical form...
Canonical XML is a normal form of XML, intended to allow relatively simple comparison of pairs of XML documents for equivalence; for this purpose, the...
because the rational canonicalform over K is also the rational canonicalform over L. This means that one may use Jordan forms that only exist over a...
transformation. The set of n × n orthogonal matrices, under multiplication, forms the group O(n), known as the orthogonal group. The subgroup SO(n) consisting...
In mathematics, a canonical basis is a basis of an algebraic structure that is canonical in a sense that depends on the precise context: In a coordinate...
generalization of row equivalence. The rank property yields an intuitive canonicalform for matrices of the equivalence class of rank k {\displaystyle k} as...
Global Information
