welldetermined

Welldetermined (often written as well-determined or well determined) is an adjective used in mathematics, statistics, and related disciplines to describe a situation in which the available information suffices to determine a result uniquely. The term is descriptive rather than a formal technical label with a single universal definition.

Usage across fields varies but generally centers on sufficiency and uniqueness. In linear algebra, a system Ax = b is considered well-determined if it has a unique solution, typically when the coefficient matrix A has full rank and the number of equations matches the number of unknowns. In statistics and inverse problems, a model is well-determined if the data uniquely identify the parameters without degeneracies such as identifiability issues. In game theory or decision problems, a scenario may be described as well-determined if optimal strategies or outcomes are uniquely determined by the rules or payoff structure.

Examples help illustrate the idea. The system x + y = 3 and 2x − y = 1 has the unique solution x = 1, y = 2, so it is well-determined. By contrast, the single equation x + y = 3 with two unknowns is underdetermined, admitting infinitely many solutions. An overdetermined system with inconsistent equations may be not solvable at all, illustrating that well-determined is often contrasted with underdetermined and overdetermined cases.

Because usage varies by discipline, welldetermined should be interpreted in context. It generally signals that the data or rules are sufficient to yield a single, stable outcome.