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Canonical is the adjective for canon, literally a 'rule', and has come to mean also 'standard', 'archetypal', 'typical', or 'unique distinguished exemplar'.
See the page canon (disambiguation) for most uses of 'canonical' in law, canon law, religion, literature, etc.
Canonical may refer to:
In mathematics, canonical example is frequently used to mean "archetype, standard example". Canonical also means "distinguished representative of a class", particularly one that does not require making any choice; this is also known as "natural", as in natural transformation. In geometry "tautological" is sometimes used as an alternative, to avoid confusion with other uses of "canonical". Specific uses of canonical include:
- Canonical coordinates, sets of coordinates which can be used to describe a physical system at any given point in time
- Canonical form, a natural unique representation of an object, or a preferred notation for some object
- Canonical homomorphism, canonical isomorphism: an homomorphism that is uniquely defined by its main property, for example, the canonical homomorphism of the integers into the rational numbers, the canonical homomorphism of a vector space onto the quotient by a subspace. More precisely, a canonical morphism or canonical homomorphism is a morphism whose existence and unicity are provided by a universal property.
- Canonical polyhedron, in geometry a polyhedron whose edges are all tangent to a common sphere, whose center is the average of its vertices; see Midsphere
- Canonical representative, in set theory a standard member of each element of a set partition
In differential geometry:
- Canonical one-form, a special 1-form defined on the cotangent bundle T*M of a manifold M
- Canonical symplectic form, the exterior derivative of this form
- Canonical vector field, the corresponding special vector field defined on the tangent bundle TM of a manifold M
- Canonical ensemble, in statistical mechanics a statistical ensemble representing a probability distribution of microscopic states of the system
- Canonical quantum gravity, an attempt to quantize the canonical formulation of general relativity
- Canonical stress-energy tensor, a conserved current associated with translations through space and time
- Canonical theory, a unified molecular theory of physics, chemistry, and biology
- Canonical variable, a conjugate variable in theoretical physics
- Canonical Huffman code, a particular type of Huffman code with unique properties which allow it to be described in a very compact manner
- Canonical link element, an HTML element that helps webmasters prevent duplicate content issues by specifying the "canonical" or "preferred" version
- Canonical Ltd., a U.K. software company
- Canonical Model, a design pattern used to communicate between different data formats
- Canonical name record (CNAME record), a type of Domain Name System record
- Canonical S-expressions, a binary encoding form of a subset of general S-expression
- Canonical XML, a normal form of XML, intended to allow relatively simple comparison of pairs of XML documents
- MAC address (formerly canonical number), a unique identifier assigned to network interfaces for communications on the physical network segment
- Pertaining to the Biblical canon
- Canonicalization a process for converting data to canonical form
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