dual,
adj. 1. (of a pair of algebraic structures) isomorphic with one another under an exchange of certain operators and perhaps constants, usually involving the distribution of negation over another operator.
2. (of a pair of operators) interchangeable in this way.
3. (of a pair of theorems) derived from one another by such an exchange.
4. (of an operator) another term for adjoint (sense 1b).
- as substantive.5. an entity related to another in one of these ways. For example, the dual of conjunction is disjunction; the dual of the proposition that P ∪ P' = U is that P ∩ P' = ∅; and the dual of a given Boolean algebra is another in which union and intersection and the null and universal sets are interchanged. 6. (of a vector space) the vector space of linear functionals on the given vector space; the dual of the dual is isomorphic to the original space. The dual of a vector space T is often written T*. 7. the vector space of all continuous linear functionals on a given topological vector space. 8. see primal-dual methods.
- as substantive.5. an entity related to another in one of these ways. For example, the dual of conjunction is disjunction; the dual of the proposition that P ∪ P' = U is that P ∩ P' = ∅; and the dual of a given Boolean algebra is another in which union and intersection and the null and universal sets are interchanged. 6. (of a vector space) the vector space of linear functionals on the given vector space; the dual of the dual is isomorphic to the original space. The dual of a vector space T is often written T*. 7. the vector space of all continuous linear functionals on a given topological vector space. 8. see primal-dual methods.