singular

Singular is an adjective and noun used in different disciplines to indicate one, unique, or exceptional. The word derives from Latin singularis, from singulus meaning one by one or single. In general use, it contrasts with plural, which denotes more than one.

In grammar, singular refers to the form used with one item (for example, “cat” vs. “cats”). Verbs and determiners often agree with the singular subject. Some nouns have irregular plural forms or mass nouns that are treated as singular in certain contexts.

In mathematics and related fields, singular denotes a loss of regularity. A singular matrix has determinant zero and is not invertible. A singular point on a curve or surface is where the usual rules fail, such as where partial derivatives vanish or curvature is undefined. In analysis, a function has a singularity at a point where it is not analytic. In physics, a gravitational singularity is a region where density or spacetime curvature becomes infinite, as in black holes.

In linear algebra, the term is used with nonsingular (invertible) and singular matrices, and with singular values in the singular value decomposition, where the values quantify scaling along orthogonal directions. In geometry and algebraic geometry, a singular variety has points where the structure is not smooth.