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Canonical is an adjective derived from canon. It essentially means "standard", "generally accepted" or "part of the back-story." An adjective is a part of speech which modifies a noun, usually describing it or making its meaning more specific. ...
In narratology, a back-story (also back story or backstory) is the history behind the situation extant at the start of the main story. ...
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 Eastern Orthodox and Roman Catholic churches, adopted by ecumenical councils. In Western culture, canon law is the law of the Roman Catholic and Anglican churches. ...
In Catholicism and Eastern Orthodoxy, an ecumenical council or general council is a meeting of the bishops of the whole church convened to discuss and settle matters of Church doctrine and practice. ...
Canonical can also mean "part of the canon", i.e., one of the books comprising the biblical canon, as opposed to apocryphal books. The Biblical canon is an exclusive list of books written during the formative period of the Jewish or Christian faiths; the leaders of these communities believed these books to be inspired by God or to express the authoritative history of the relationship between God and his people (although there may...
Apocrypha is a Greek word (απόκÏυφα, neuter plural of απόκÏυφος), from αποκÏυπτειν, to hide away. ...
Literature and art It is used most often when describing bodies of literature or art: those books that all educated people have read make up the "canon" (see also canon (fiction)). In the context of fiction, the canon of a fictional universe comprises those novels, stories, films, etc. ...
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.") Look up Up to on Wiktionary, the free dictionary In mathematics, the phrase up to xxxx indicates that members of an equivalence class are to be regarded as a single entity for some purpose. ...
A prime number (or a prime) is a natural number that only has trivial divisors. ...
In mathematics, factorization or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. ...
The integers consist of the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero. ...
In 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 simplified into a standard...
In mathematics, a matrix (plural matrices) is a rectangular table of numbers or, more generally, of elements of a ring-like algebraic structure. ...
In linear algebra, one associates a polynomial to every square matrix, its characteristic polynomial. ...
In mathematics, especially in abstract algebra and related areas, a permutation is a bijection from a finite set X onto itself. ...
In abstract algebra, a homomorphism is a structure-preserving map. ...
In mathematics, a group is a set, together with a binary operation, such as multiplication or addition, satisfying certain axioms, detailed below. ...
In mathematics, an isomorphism (in Greek isos = equal and morphe = shape) is a kind of mapping between objects, devised by Eilhard Mitscherlich, which shows a relation between two properties or operations. ...
A vector space (or linear space) is the basic object of study in the branch of mathematics called linear algebra. ...
Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. ...
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). A vector space (or linear space) is the basic object of study in the branch of mathematics called linear algebra. ...
In linear algebra, the standard basis for an -dimensional vector space is the basis obtained by taking the basis vectors where is the vector with a in the th coordinate and elsewhere. ...
In mathematics, a linear transformation (also called linear operator or linear map) is a function between two vector spaces that respects the arithmetical operations addition and scalar multiplication defined on vector spaces, or, in other words, it preserves linear combinations. Definition and first consequences Formally, if V and W are...
In mathematics, Euclidean space is a generalization of the 2- and 3-dimensional spaces studied by Euclid. ...
In 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 simplified into a standard...
The word canonical is also used for a preferred way of writing something, see the main article canonical form. Generally, in mathematics, a canonical form is a function that is written in the most standard, conventional, and logical way. ...
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). Computer science is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ...
In computing, a file system is a method for storing and organizing computer files and the data they contain to make it easy to find and access them. ...
For the various types of hierarchy, see hierarchy (disambiguation) A hierarchy (in Greek: ΙεÏαÏχία, it is derived from ιεÏός-hieros, sacred, and άÏχω-arkho, rule) is a system of ranking and organizing things or people, where each element of the system (except for the top element) is subordinate to a single other element. ...
This article just presents the basic definitions. ...
XML Signature (also called XMLDsig) is a W3C recommendation that defines an XML syntax for digital signatures. ...
The Extensible Markup Language (EML) is a W3C-recommended general-purpose markup language for creating special-purpose markup languages, capable of describing many different kinds of data. ...
The Java Web Services Development Pack (JWSDP) is a free Software Development Kit (SDK) for developing Web Services, web applications and Java applications with the newest technologies for Java. ...
For an illuminating story about the word's use among computer scientists, see the Jargon File's entry for the word[1]. The Jargon File is a glossary of hacker slang. ...
Some people have been known to use the word canonicality; others use canonicity. In fields other than computer science, canonicity is this word's canonical form.
The company Canonical Ltd is named jocularly referencing this usage. Canonical Ltd is a private company founded (and funded) by South African entrepreneur Mark Shuttleworth for the promotion of Free Software projects. ...
Physics In theoretical physics, the concept of canonical (or 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. The existence of such coordinates is guaranteed under fairly 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 symmetry in a variable implies an invariance of the conjugate variable, and vice versa; for instance symmetry under time reversal is followed by energy conservation. Theoretical physics employs mathematical models in an attempt to understand Nature. ...
A Superconductor demonstrating the Meissner Effect. ...
A spatial point is an entity with a location in space but no extent (volume, area or length). ...
In physics, momentum is the product of the mass and velocity of an object. ...
This article is about angles in geometry. ...
In physics the angular momentum of an object with respect to a reference point is a measure for the extent to which, and the direction in which, the object rotates about the reference point. ...
Watches are used to measure time Time has long been a major subject of philosophy, art, poetry, and science. ...
In mathematics and classical mechanics, the Poisson bracket is an important operator in Hamiltonian mechanics, playing a central role in the definition of the time-evolution of a dynamical system in the Hamiltonian formulation. ...
In mathematics, the Kronecker delta or Kroneckers delta, named after Leopold Kronecker (1823-1891), is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise. ...
Darbouxs theorem is a theorem in symplectic topology which states that every symplectic manifold (of fixed dimension) is locally symplectomorphic. ...
Hamiltonian mechanics is a re-formulation of classical mechanics that was invented in 1833 by William Rowan Hamilton. ...
A simple introduction to this subject is provided in Basics of quantum mechanics. ...
In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the time-dependence of quantum mechanical systems. ...
In quantum physics, the Heisenberg uncertainty principle states that one cannot assign, with full precision, values for certain pairs of observable variables, including the position and momentum, of a single elementary particle at the same time even in theory. ...
Noethers theorem is a central result in theoretical physics that expresses the one-to-one correspondence between symmetries and conservation laws. ...
Square with symmetry group D4 Symmetry is a characteristic of geometrical shapes, equations, and other objects; we say that such an object is symmetric with respect to a given operation if this operation, when applied to the object, does not appear to change it. ...
In physics, invariants are usually quantities conserved (unchanged) by the symmetries of the physical system. ...
Wikipedia does not have an article with this exact name. ...
Conservation of energy is possibly the most important, and certainly the most practically useful of several conservation laws in physics. ...
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. Statistical mechanics is the application of statistics, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ...
A canonical ensemble in statistical mechanics is an ensemble of dynamically similar systems, each of which can share its energy with a large heat reservoir, or heat bath. ...
In statistical mechanics, the grand canonical ensemble is a statistical ensemble, that means a set of identically prepared systems, each of which is in equilibrium with an external bath with respect to particle and energy exchange. ...
The microcanonical ensemble is the simplest of the ensembles of statistical mechanics, in which many replicas of a system are assumed to be confined to a region of phase space of constant energy. ...
In mathematics, a probability distribution assigns to every interval of the real numbers a probability, so that the probability axioms are satisfied. ...
In statistical mechanics, a microstate describes a specific detailed microscopic configuration of a system, that the system visits in the course of its thermal fluctuations. ...
Thermodynamics (from the Greek thermos meaning heat and dynamis meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ...
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