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 transformation or hatching, involving a conspicuous and relatively abrupt change in the animal's body structure through cell growth and different ...

, 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 t ...

, genetic alteration of a cell by DNA uptake

In mathematics

Transformation (function) In mathematics, a transformation, transform, or self-map 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 trans ...

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

function (mathematics) In mathematics, a function from a set (mathematics), set to a set assigns to each element of exactly one element of .; the words ''map'', ''mapping'', ''transformation'', ''correspondence'', and ''operator'' are sometimes used synonymously. ...

. **

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 general ...

, 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 pr ...

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 there exists an m \times n matrix A, called the transfo ...

which represent linear maps in linear algebra. *

Integral transform In mathematics, an integral transform is a type of transform that 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 charac ...

, 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 linear isomorphism 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 precise ...

, 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, such as preserving distances, angles, or ratios (scale). More specifically, it is a function wh ...

, 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 ...

, a limiting case of a geometrical transformation

In physics and chemistry

* Chemical transformation *

Phase transformation In physics, chemistry, and other related fields like biology, 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 s ...

, a physical transition between states of matter * Transformation optics, generalized optical devices * Unitary transformation (quantum mechanics)

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 labo ...

, in economics *

Transformation (linguistics) In linguistics, transformational grammar (TG) or transformational-generative grammar (TGG) was the earliest scientific modelling, model of grammar proposed within the research tradition of generative grammar. Like current generative theories, it tr ...

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

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 functi ...

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 ana ...

* ''Transformation'' (Don Preston album) * ''Transformation'' (Tal Wilkenfeld album) * ''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, Tran ...

* ''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 Amazing World of Gumball''), an episode of the British-American animated television series ''The Amazing World of Gumball'' * " The Transformation", an episode of American television series ''Fringe'' * Transformation playing card * "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 o ...

, 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, a design process *

Transformational leadership Transformational leadership is a leadership style in which a leader's behaviors influence their followers, inspiring them to perform beyond their perceived capabilities. This style of leadership encourages individuals to achieve unexpected or rem ...

, 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 (DT) is the process of adoption and implementation of digital technology by an organization in order to create new or modify existing products, services and operations by the means of translating business processes into a d ...

In computing

* Data transformation (computing) *

Model transformation A model transformation, in model-driven engineering, is an automated way of modifying and creating platform-specific model from platform-independent ones. An example use of model transformation is ensuring that a family of models is consistent, in ...

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 of p ...

* XML transformation * Transformation of text

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 and in workplaces 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 ...

* Transformational festival *

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, shapeshifting is the ability to physically transform oneself through unnatural means. The idea of shapeshifting is found in the oldest forms of totemism and shamanism, as well as the oldest existen ...

, a mythological ability of humans to ''transform'' into animals, hybrid creatures, etc. * Clinical lycanthropy, a delusion that one can actually ''transform'' into an animal