Transformationsrechnung

Transformation refers to a process by which something undergoes a change in form, structure, or function. The term is used across disciplines to describe alterations in geometry, biology, information, culture, and systems.

In mathematics, a transformation is a function that maps elements from one set to another, often preserving structure. Geometric transformations include translations, rotations, reflections, and scaling. Linear transformations are represented by matrices and act on vector spaces. Affine transformations combine linear maps with translations, preserving parallelism. Transformations can be classified by properties such as invertibility and fixed points.

In biology, transformation denotes the uptake and incorporation of foreign DNA by a cell, leading to genetic change. It is a fundamental technique in molecular biology and genetic engineering. Methods include chemical competence and electroporation, which permeabilize cell membranes to DNA.

In computing, data transformation converts data from one format or structure into another, facilitating integration and analysis. ETL processes use extraction, transformation, and loading steps. Transformation rules may include normalization, filtering, and encoding.

In sociology and business, transformation refers to substantial changes in institutions, practices, or culture. Digital transformation describes the integration of digital technology into all areas of an organization to improve performance and value.

In physics and engineering, coordinate transformations relate measurements between different reference frames, as in Lorentz or Galilean transformations. These concepts underpin how observers describe the same phenomena under different conditions.