Tensorwertig

Tensorwertig is a German adjective used in mathematics and physics to describe a quantity, object, or function whose values are tensors rather than scalars or vectors. In this sense, a tensorwertiges Objekt is tensor-valued.

In mathematical contexts, tensorwertig typically refers to tensor-valued functions or fields. A function or field f defined on a domain maps each point to a tensor in a chosen type (for example, T^p_q(V)). The simplest examples are tensor-valued fields on a manifold or region, such as a second-order tensor field representing stress or diffusion.

In physics and differential geometry, many fundamental quantities are tensorwertig. Examples include the stress tensor in continuum mechanics, the Riemann curvature tensor in geometry, and the electromagnetic field tensor in relativity. The rank or order of the tensor indicates how many indices it carries and governs its transformation behavior under coordinate changes and how it contracts with other tensors.

The term is standard in German-language texts; in English, the corresponding expression is tensor-valued or tensor-valued function/field. The underlying concept is the same across languages: an object whose values lie in a tensor space rather than in the scalar or vector spaces.