Transformation may refer to:

Science and mathematics

In biology and medicine

Metamorphosis Metamorphosis is a biological process by which an animal physically develops including birth or hatching, involving a conspicuous and relatively abrupt change in the animal's body structure through cell growth and differentiation. Some inse ...

, the biological process of changing physical form after birth or hatching *

Malignant transformation Malignant transformation is the process by which cells acquire the properties of cancer. This may occur as a primary process in normal tissue, or secondarily as ''malignant degeneration'' of a previously existing benign tumor. Causes There are ...

, the process of cells becoming cancerous *

Transformation (genetics) In molecular biology and genetics, transformation is the genetic alteration of a cell resulting from the direct uptake and incorporation of exogenous genetic material from its surroundings through the cell membrane(s). For transformation to ta ...

, genetic alteration of a cell by DNA uptake

In mathematics

Transformation (function) In mathematics, a transformation is a function ''f'', usually with some geometrical underpinning, that maps a set ''X'' to itself, i.e. . Examples include linear transformations of vector spaces and geometric transformations, which include proj ...

, concerning functions from sets to themselves. For functions in the broader sense, see

function (mathematics) In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the funct ...

. **

Affine transformation In Euclidean geometry, an affine transformation or affinity (from the Latin, ''affinis'', "connected with") is a geometric transformation that preserves lines and parallelism, but not necessarily Euclidean distances and angles. More generally, ...

, in geometry **

Linear transformation In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V \to W between two vector spaces that pre ...

between modules in linear algebra. Also called a linear map. ***

Transformation matrix In linear algebra, linear transformations can be represented by matrices. If T is a linear transformation mapping \mathbb^n to \mathbb^m and \mathbf x is a column vector with n entries, then T( \mathbf x ) = A \mathbf x for some m \times n matrix ...

which represent linear maps in linear algebra. *

Integral transform In mathematics, an integral transform maps a function from its original function space into another function space via integration, where some of the properties of the original function might be more easily characterized and manipulated than in ...

, between a function in one domain to a function in another *

Natural transformation In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal structure (i.e., the composition of morphisms) of the categories involved. Hence, a natur ...

between functors in category theory. *

Unitary transformation In mathematics, a unitary transformation is a transformation that preserves the inner product: the inner product of two vectors before the transformation is equal to their inner product after the transformation. Formal definition More precisely, ...

, between two Hilbert spaces *

Geometric transformation In mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning. More specifically, it is a function whose domain and range are sets of points — most often ...

, between sets of points in geometry **

Infinitesimal transformation In mathematics, an infinitesimal transformation is a limiting form of ''small'' transformation. For example one may talk about an infinitesimal rotation of a rigid body, in three-dimensional space. This is conventionally represented by a 3×3 ske ...

, a limiting case of a geometrical transformation

In physics and chemistry

Chemical transformation A chemical substance is a form of matter having constant chemical composition and characteristic properties. Some references add that chemical substance cannot be separated into its constituent elements by physical separation methods, i.e., wi ...

Phase transformation In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...

, a physical transition from one medium to another *

Transformation optics Transformation optics is a branch of optics which applies metamaterials to produce spatial variations, derived from coordinate transformations, which can direct chosen bandwidths of electromagnetic radiation. This can allow for the construction ...

, generalized optical devices *

Unitary transformation (quantum mechanics) In quantum mechanics, the Schrödinger equation describes how a system changes with time. It does this by relating changes in the state of system to the energy in the system (given by an operator called the Hamiltonian). Therefore, once the Hamil ...

In other sciences

Transformation problem In 20th-century discussions of Karl Marx's economics, the transformation problem is the problem of finding a general rule by which to transform the "values" of commodities (based on their socially necessary labour content, according to his labou ...

, a concept in economics *

Transformation (linguistics) In linguistics, transformational grammar (TG) or transformational-generative grammar (TGG) is part of the theory of generative grammar, especially of natural languages. It considers grammar to be a system of rules that generate exactly those combi ...

, a type of operation in transformational grammar * Transformation of precious metals, see

synthesis of precious metals The synthesis of precious metals involves the use of either nuclear reactors or particle accelerators to produce these elements. Precious metals occurring as fission products Ruthenium, rhodium Ruthenium and rhodium are precious metals produce ...

Data transformation (statistics) In statistics, data transformation is the application of a deterministic mathematical function to each point in a data set—that is, each data point ''zi'' is replaced with the transformed value ''yi'' = ''f''(''zi''), where ''f'' is a functio ...

Arts and entertainment

In music

Transformation (music) In music, a transformation consists of any operation or process that may apply to a musical variable (usually a set or tone row in twelve tone music, or a melody or chord progression in tonal music), or rhythm in composition, performance, or anal ...

* ''Transformation'' (Don Preston album), 2001 * ''Transformation'' (Tal Wilkenfeld album), 2007 * ''Transformation'' (Signal Aout 42 album) *

Transformation (Alex Skolnick Trio album) Alex Skolnick (born September 29, 1968) is an American musician. He is best known as the lead guitarist and one of the songwriters of the thrash metal band Testament and has played with several other bands, including The Alex Skolnick Trio, Tra ...

* "Transformation", a song by

Nona Hendryx Nona Bernis Hendryx (born October 9, 1944) is an American vocalist, record producer, songwriter, musician, and author. Hendryx is known for her work as a solo artist as well as for being one-third of the trio Labelle, who had a hit with "Lady ...

* ''Transformations'' (opera), a chamber opera by the American composer Conrad Susa * ''The Transformation'' (album)

In other arts and entertainment

* ''Transformation'' (novel), by Carol Berg * ''Transformation'', an alternate title for ''

The Marble Faun ''The Marble Faun: Or, The Romance of Monte Beni'', also known by the British title ''Transformation'', was the last of the four major romances by Nathaniel Hawthorne, and was published in 1860. ''The Marble Faun'', written on the eve of the Ame ...

'', a novel by Nathaniel Hawthorne * "

The Transformation "The Transformation" is the thirteenth episode of the first season of the American science fiction drama television series ''Fringe''. Its storyline centers on the circumstances surrounding a deceased scientist (Neal Huff), who was doped with a ...

", an episode of American television series ''Fringe'' *

Transformation playing card A transformation playing card (sometimes referred to as a transformation deck when assembled into a complete set) is a type of playing card where an artist incorporates the pips of the non-face cards into an artistic design. In a classical trans ...

* "Transformation" (short story), a short story by Mary Shelley

In business and technology

In business

Business transformation In management it has been said that business transformation involves making fundamental changes in how business is conducted in order to help cope with shifts in market environment. However this is a relatively narrow definition that overlooks ot ...

, a major change in the identity, structure, or purpose of an organization (from the field of strategic management) *

Transformation (law) In United States copyright law, transformative use or transformation is a type of fair use that builds on a copyrighted work in a different manner or for a different purpose from the original, and thus does not infringe its holder's copyright. Tr ...

, a concept in copyright law * Transformation (patent law) *

Transformation design In broad terms, transformation design is a human-centered, interdisciplinary process that seeks to create desirable and sustainable changes in behavior and form – of individuals, systems and organizations. It is a multi-stage, iterative proces ...

, a design process *

Transformational leadership Transformational leadership is a theory of leadership where a leader works with teams or followers beyond their immediate self-interests to identify needed change, creating a vision to guide the change through influence, inspiration, and executing t ...

, a managerial approach emphasizing organizational change *

Maturity transformation Maturity transformation is the practice by financial institutions of borrowing money on shorter timeframes than they lend money out. Financial markets also have the effect of maturity transformation whereby investors such as shareholders and bondhol ...

, the practice of fractional reserve banks borrowing money on shorter timeframes than they lend money out *

Digital transformation Digital transformation is the adoption of digital technology by an organization to digitize non-digital products, services or operations. The goal for its implementation is to increase value through innovation, invention, customer experience or ef ...

In computing

Data transformation In computing, data transformation is the process of converting data from one format or structure into another format or structure. It is a fundamental aspect of most data integrationCIO.com. Agile Comes to Data Integration. Retrieved from: http ...

Model transformation A model transformation, in model-driven engineering, is an automated way of modifying and creating models. An example use of model transformation is ensuring that a family of models is consistent, in a precise sense which the software engineer can ...

Program transformation A program transformation is any operation that takes a computer program and generates another program. In many cases the transformed program is required to be semantically equivalent to the original, relative to a particular formal semantics and ...

XML transformation An XML transformation language is a programming language designed specifically to transform an ''input'' XML document into an ''output'' document which satisfies some specific goal. There are two special cases of transformation: * XML to XML: ...

Transformation of text Transformations of text are strategies to perform geometric transformations on text (reversal, rotations, etc.), particularly in systems that do not natively support transformation, such as HTML, seven-segment displays and plain text. Implementa ...

Other uses

* ''Transformation'' (journal), an academic journal in the field of Biblical studies * Transformation (warfare) *

Transformation of culture Culture change is a term used in public policy making that emphasizes the influence of cultural capital on individual and community behavior. It has been sometimes called repositioning of culture, which means the reconstruction of the cultural conce ...

Transformational festival A transformational festival is a counterculture festival that espouses a community-building ethic, and a value system that celebrates life, personal growth, social responsibility, healthy living, and creative expression. ''Transformational'' allud ...

Spiritual transformation Spiritual transformation involves a fundamental change in a person's sacred or spiritual life. Psychologists examine spiritual transformation within the context of an individual's ''meaning system'', Israela Silberman (2005)Religion as a meanin ...

, a fundamental change in an individual (a psychological and New-Age concept) *

Shapeshifting In mythology, folklore and speculative fiction, shape-shifting is the ability to physically transform oneself through an inherently superhuman ability, divine intervention, demonic manipulation, Magic (paranormal), sorcery, Incantation, ...

, a type of transformation common in mythology and folklore