Transformation

Transformation refers to the process of changing in form, structure, appearance, or condition. It is used across many fields to describe both concrete alterations and abstract changes in meaning or role. Depending on the context, a transformation may be reversible or irreversible, partial or complete, and it may preserve some properties while altering others.

In mathematics, a transformation is a mapping from one set to another that preserves some specified structure. Geometric transformations include translations, rotations, reflections, and scalings, which move or resize objects in space. A transformation is often described by a function or matrix; when a transformation preserves distances it is called an isometry, and when it preserves straight lines and ratios it is affine or similarity transformation. The composition of transformations and their inverses are central ideas in geometry and linear algebra.

In science and engineering, transformations describe changes in data or representations. Data transformation converts data from one format or structure to another, often as part of preparation for analysis. In signal processing, transforms such as the Fourier or Laplace transforms decompose signals into alternative representations.

In biology, transformation refers to the uptake and expression of genetic material by an organism, a process used in genetic engineering and in nature through horizontal gene transfer. The term also appears in developmental biology to describe changes in cell fate and tissue remodeling as organisms grow.

In social sciences and business, transformation denotes large-scale change in systems, institutions, or individuals. Digital transformation, organizational transformation, and personal transformation refer to coordinated efforts to alter practices, culture, or capabilities to achieve new goals.

In culture and the arts, transformation is a common motif and technique, signaling metamorphosis, adaptation, or reinterpretation of forms, often explored through literature, theater, and visual arts.