In mathematics, a rule for changing a geometric figure or algebraic expression into another, usually accompanied by a rule for transforming it back. In geometry and topology, a transformation (e.g., flipping horizontally or vertically, rotating, or stretching vertically or horizontally) moves each point in a figure or graph to another position. A graph also undergoes a transformation when its coordinate system is changed. For example, the equations that establish a correspondence between the rectangular and polar coordinate systems constitute a transformation. In analysis, a transformation is a procedure that changes one function into another. Of special interest in many fields of mathematics are transformations forming a group, in which any two transformations applied successively produce the same result as another transformation in the group and each transformation has an inverse transformation (which undoes it) in the group. Seealso group theory, integral transform, linear transformation.

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Transformation (root transform) may refer to: Transformation is also referred to as a turn.

In science:

• Transformation (geometry), in mathematics, as a general term applies to mathematical functions.
• Data transformation (statistics) in statistics.
• Chemical transformation, in chemistry, shows the conversion of a substrate to a product omitting the reagents or catalysts.
• Transformation (genetics), the genetic alteration of a cell resulting from the introduction of foreign DNA.
• Transformational grammar, in linguistics.
• Malignant Transformation, the first step in Tumorigenesis, converts normal cells into cells that will continue to divide without limit (cancerous cells). Transformation can also refer to the development of a higher grade (more aggressive) case, especially in blood-related neoplasms, when it is called Richter's transformation or Richter's syndrome.
• Metamorphosis (biology), post-natal biological transformation.

In computing:

• Data transformation, process of converting data from a source into a destination format.
• Model transformation, process of converting a model Ma conforming to metamodel MMa into model Mb conforming to metamodel MMb. If MMa=MMb, then one has an endogeneous transformation; otherwise one has an exogeneous transformation. Model transformation usually takes place using languages like GReAT, VIATRA, ATL, etc.
• Program transformation, the process of converting special source code into other detailed structures.
• Vocabulary-based transformation.
• XML transformation language, process of transforming an XML document into another one with languages like XSLT, XQuery, STX, FXT, XDuce, HaXml, FleXML, etc.

In fiction:

• Shapeshifting, the change of an entity into another in myth and in fiction.
• Henshin, a visual sequence for transformation occurring in many anime, manga and sentai tokusatsu.
• Mutating in fiction
• Transformation (novel), a 2000 novel by Carol Berg.
• Transformation Story Archive, a website that archives stories that feature a personal physical transformation.

In other subjects:

• Change, especially extreme psychological or character change, as in the context and vocabulary of pop psychology.
• Spiritual transformation
• Transformation (philosophical), the shift in context and being that requires no change in circumstance.
• Transformation (law), a principle that contributes to a finding of fair use in the United States.
• Transformation design, a human-centered, interdisciplinary process that seeks to create desirable and sustainable changes in behavior and form – of individuals, systems and organizations – often for socially progressive ends.
• Transformation (music), any operation or process that a composer or performer may apply to a musical variable.
• Transformation (warfare), the introduction and use of seemingly revolutionary methods of mainly strategic nature to gain a permanent advantage over a perceived enemy.
• Transformation (UK Company), A retail chain provising products and services to the transgender community.
• Text Transformation (English Literature), the process of taking a foundation, or base text and changing it into a new genre, so that it can support itself without reference to the base text.
• Transformation playing card, a type of playing card where the pips are incorporated into an artistic design.
• Transformation Journal Transformation is an established journal serving as a forum for analysis and debate about South African society in transition, as well as the surrounding region, and the global context that affects southern African developments.
• Transformation problem A theory of the value of commodities proposed by Karl Marx.
• Transformation of culture How cultures worldwide are undergoing change due to internal and external forces.
• Business Network Transformation, expansion of a business' market through business networks with partners, suppliers, and customers.

See also

• Trans-
• Transmigration