# Dictionary Definition

canonical adj

1 appearing in a Biblical canon; "a canonical
book of the Christian New Testament" [syn: canonic]

2 of or relating to or required by canon law
[syn: canonic]

3 reduced to the simplest and most significant
form possible without loss of generality; "a basic story line"; "a
canonical syllable pattern" [syn: basic, canonic]

4 conforming to orthodox or recognized rules;
"the drinking of cocktails was as canonical a rite as the mixing"-
Sinclair Lewis [syn: canonic, sanctioned]

# User Contributed Dictionary

## English

### Etymology

### Adjective

- Present in a canon of
Scripture.
- The Gospel of Luke is a canonical New Testament book.

- In conformity with canon law.
- According to recognised or orthodox rules.
- The men played golf in the most canonical way, with no local rules.

- Stated or used in the most basic and straightforwardly
applicable manner.
- This definition would be more useful if it were canonical.

- In the form of a canon.
- Of or pertaining to an ecclesiastical chapter
- In the context of "math|compsci": In canonical form.

#### Antonyms

# Extensive Definition

Canonical is an adjective derived from
canon.
Canon comes from the Greek word kanon "rule" (perhaps originally
from kanna "reed", cognate to cane) is used in various
meanings.

basic, canonic, canonical: reduced to the
simplest and most significant form possible without loss of
generality, e.g. "a basic story line"; "a canonical syllable
pattern"

## Religion

This word is used by theologians and canon lawyers to refer to the canons of the Roman Catholic, Eastern Orthodox and Anglican Churches adopted by ecumenical councils. It also refers to later law developed by local churches and dioceses of these churches. The function of this collection of various "canons" is somewhat analogous to the precedents established in common law by case law.In the 20th century, the Roman Catholic Church
revised its canon law in 1917 and then again 1981 into the modern
Code of Canon Law. This code is no longer merely a compilation
of papal decrees and conciliar legislation, but a more completely
developed body of international church law. It is analogous to the
English system of Statute law.

Canonical can also mean "part of the canon",
i.e., one of the books comprising a biblical
canon, as opposed to apocryphal books.

The term is also applied by Westerners to other
religions, but in inconsistent ways: for example, in the case of
Buddhism one authority refers to "scriptures and other canonical
texts", while another says that scriptures can be categorized into
canonical, commentarial and pseudo-canonical.

Canonization is the process by which a person is
recognized as a saint.

## Literature and art

The word is also often used when describing bodies of literature or art: those books that all educated people have supposedly read, or are advised to read, make up the "canon", for example the Western canon. (See also canon (fiction)).## Mathematics

Mathematicians have for perhaps a century or more used the word canonical to refer to concepts that have a kind of uniqueness or naturalness, and are (up to trivial aspects) "independent of coordinates." Examples include the canonical prime factorization of positive integers, the Jordan canonical form of matrices (which is built out of the irreducible factors of the characteristic polynomial of the matrix), and the canonical decomposition of a permutation into a product of disjoint cycles. Various functions in mathematics are also canonical, like the canonical homomorphism of a group onto any of its quotient groups, or the canonical isomorphism between a finite-dimensional vector space and its double dual. Although a finite-dimensional vector space and its dual space are isomorphic, there is no canonical isomorphism. This lack of a canonical isomorphism can be made precise in terms of category theory, but one could say at a simpler level that "any isomorphism you can think of here depends on choosing a basis." As stated by Goguen, "To any canonical construction from one species of structure to another corresponds an adjunction between the corresponding categories."Being canonical in mathematics is stronger than
being a conventional choice. For instance, the vector space
Rn has a standard
basis which is canonical in the sense that it is not just a
choice which makes certain calculations easy; in fact most linear
operators on Euclidean
space take on a simpler form when written as a matrix relative
to some basis other than the standard one (see Jordan form).
In contrast, an abstract n-dimensional real vector space V would
not have a canonical basis; it is isomorphic to Rn of course, but
the choice of isomorphism is not canonical.

The word canonical is also used for a preferred
way of writing something, see the main article canonical
form.

In set theory, the term "canonical" identifies an
element as representative of a set. If a set is partitioned
into equivalence
classes, then one member can be chosen from each equivalence
class to represent that class. That representative member is the
canonical member. If you have a canonicalizing function, f(x), that
maps x to the canonical member of the equivalence class which
contains it, then testing whether two items, a and b, are
equivalent is the same as testing whether f(a) is identical to
f(b).

## Computer science

Some circles in the field of computer science have borrowed this usage from mathematicians. It has come to mean "the usual or standard state or manner of something"; for example, "the canonical way to organize a file system is as a hierarchy, with extensions to make it a directed graph". XML Signature defines canonicalization as the process of converting XML content to a canonical form, to take into account changes that can invalidate a signature over that data (from JWSDP 1.6).In
enterprise application integration, the "canonical data model"
is a design
pattern used to communicate between different data formats. It
introduces an additional format, called the "canonical format",
"canonical document type" or "canonical data model". Instead of
writing translators between each and every format (with potential
for a combinatorial
explosion), it is sufficient just to write a translator between
each format and the canonical format. The Open Applications Group
Integration Specification (OAGIS) is an example
of an integration architecture that is based on a canonical data
model.

For an illuminating story about the word's use
among computer scientists, see the Jargon File's
entry for the wordhttp://catb.org/~esr/jargon/html/C/canonical.html.

Some people have been known to use the noun
canonicality; others use canonicity. In fields other than computer
science, canonicity is this word's canonical form.

In computer science, a canonical name record (or
CNAME) is a
type of DNS record.

In computer science, a canonical number is the
old designation for a MAC code on routers and servers.

## Physics

In theoretical physics, the concept of canonical (or conjugate, or canonically conjugate) variables is of major importance. They always occur in complementary pairs, such as spatial location x and linear momentum p, angle φ and angular momentum L, and energy E and time t. They can be defined as any coordinates whose Poisson brackets give a Kronecker delta (or a Dirac delta in the case of continuous variables). The existence of such coordinates is guaranteed under broad circumstances as a consequence of Darboux's theorem. Canonical variables are essential in the Hamiltonian formulation of physics, which is particularly important in quantum mechanics. For instance, the Schrödinger equation and the Heisenberg uncertainty relation always incorporate canonical variables. Canonical variables in physics are based on the aforementioned mathematical structure and therefore bear a deeper meaning than being just convenient variables. One facet of this underlying structure is expressed by Noether's theorem, which states that a (continuous) symmetry in a variable implies an invariance of the conjugate variable, and vice versa; for instance symmetry under spatial displacement leads to conservation of momentum, and time-independence implies energy conservation.In statistical
mechanics, the canonical
ensemble, the grand
canonical ensemble, and the microcanonical
ensemble are archetypal probability
distributions for the (unknown)
microscopic state of a thermal system, applying respectively in
the physical cases of:- a closed system at fixed temperature (able
to exchange energy with its environment); an open system at fixed
temperature (able to exchange both energy and particles); and a
closed thermally isolated system (able to exchange neither). These
probability distributions can be applied directly to practical
problems in thermodynamics.

## See also

- Literary canons and Canon (fiction)
- Canonicalization is a transformation to get the canonical form.

## References

canonical in German: Kanonisch

canonical in French: Canonique

canonical in Ido: Kanonala

canonical in Turkish: Kanonik

# Synonyms, Antonyms and Related Words

Biblical, Christian, Gospel, Mariological, Mosaic, New-Testament,
Old-Testament, abbatial, abbatical, accepted, apocalyptic, apostolic, approved, archiepiscopal, authentic, authoritative, binding, canonic, capitular, capitulary, churchly, clerical, confessional, conventional, correct, creedal, customary, dictated, didactic, divine, doctrinal, doctrinary, dogmatic, ecclesiastic, episcopal, episcopalian, evangelic, evangelical, evangelistic, faithful, firm, formulary, gospel, hard and fast, inspired, instructive, literal, mandatory, ministerial, of the faith,
official, orthodox, orthodoxical, pastoral, physicotheological,
preceptive, prelatial, prelatic, prescribed, prescript, prescriptive,
priest-ridden, priestish, priestly, proper, prophetic, rabbinic, received, regulation, religious, revealed, revelational, right, rubric, sacerdotal, sanctioned, scriptural, sound, standard, statutory, textual, textuary, theological, theopneustic, traditional, traditionalistic,
true, true-blue, ultramontane