Dual system
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This article is about dual pairs of vector spaces. For dual pairs in representation theory, see Reductive dual pair.
In mathematics, a dual system, dual pair or a duality over a field is a triple consisting of two vector spaces and over and a non-degenerate bilinear map .
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Mathematical duality theory, the study of dual systems, has an important place in functional analysis and has extensive applications to quantum mechanics via the theory of Hilbert spaces.