Complex conjugate of a vector space

In mathematics, the complex conjugate of a complex vector space V {\displaystyle V\,} is a complex vector space V ¯ {\displaystyle {\overline {V}}} that has the same elements and additive group structure as V , {\displaystyle V,} but whose scalar multiplication involves conjugation of the scalars. In other words, the scalar multiplication of V ¯ {\displaystyle {\overline {V}}} satisfies α ∗ v = α ¯ ⋅ v {\displaystyle \alpha \,*\,v={\,{\overline {\alpha }}\cdot \,v\,}} where ∗ {\displaystyle *} is the scalar multiplication of V ¯ {\displaystyle {\overline {V}}} and ⋅ {\displaystyle \cdot } is the scalar multiplication of V .

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