Transformatievorm

Transformatievorm is a term used in Dutch mathematical and scientific contexts to describe the representation of an object after a transformation has been applied. The focus is on how the object’s coordinates, structure, or relationships change, while essential properties may be preserved or tracked as invariants.

In linear algebra, a transformatievorm often refers to the matrix form of a linear transformation after a change of basis. Common transformed forms include diagonal, triangular, or Jordan forms. These representations can simplify tasks such as solving systems of equations, computing eigenvalues, or classifying the transformation or the associated vector space.

More generally, transformatievorm covers coordinate changes in geometry and analysis, where a function, vector, or geometric figure is expressed in a different coordinate system or under a geometric operation such as rotation, reflection, translation, or scaling. The transformed form can reveal properties that are not apparent in the original presentation.

In data processing and signal analysis, transformations produce transformatieve vormen of data, exposing frequency components, patterns, or structures that aid interpretation, compression, or further processing.

The term is primarily used in Dutch-language literature; in English, the concept is usually described as a transformed form, a representation after a transformation, or a canonical/normal form, depending on context.

See also: transformation, change of basis, canonical form, normal form, diagonalization, invariants.