An antilinear map (or antilinear transformation) is a type of function between two vector spaces that preserves the structure of the spaces in a specific way, but differs from a linear map in terms of how it handles scalar multiplication.
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For complex vector spaces, an antilinear map satisfies . It is linear over the real numbers and conjugates complex scalar multiplication. This differs from two conjugate linear operators, which are related by similarity rather than conjugate-linearity.