Complex conjugate vector space

In mathematics, the complex conjugate of a complex vector space ${\displaystyle V\,}$ is a complex vector space ${\displaystyle {\overline {V}}}$, which has the same elements and additive group structure as ${\displaystyle V}$, but whose scalar multiplication involves conjugation of the scalars. In other words, the scalar multiplication of ${\displaystyle {\overline {V}}}$ satisfies

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