singulár

Singulær is an adjective used in Norwegian to describe something that is single, unique, or exceptional, and it serves as a technical term in several disciplines. The word derives from Latin singularis, through French singulier, and has been adopted in modern Scandinavian languages to convey notions of distinctiveness or deviation from the norm.

In mathematics and related fields, singulær denotes an exceptional or non-standard case. A singular point of a function or a curve is a location where ordinary rules fail, such as a point where a derivative does not exist or where the curve has a cusp or self-intersection. A singular matrix is a square matrix with determinant zero, hence non-invertible. The concept extends to linear algebra via singular values in singular value decomposition, and to algebraic geometry and differential equations through singularities and singular solutions, which are solutions that cannot be obtained by standard integration techniques.

In physics, a singularity refers to a point where physical quantities become infinite or ill-defined, such as infinite density or curvature. Gravitational singularities are predicted by general relativity in contexts like the centers of black holes or the origin of the universe (the Big Bang). The presence of singularities signals the limits of classical theories and motivates the search for quantum-gravity descriptions.

Other uses can be found in analysis and modelling, where a problem exhibits degeneracy or undefined behavior that requires special treatment. In Norwegian grammar, the standard term for singular is entall, with singulær used mainly in mathematical or descriptive contexts to indicate exceptional or unique cases.