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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 ¯…

Complex conjugate of a Hilbert space, Motivation & Complex conjugation functor

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Complex conjugate of a Hilbert space

Hilbert spaceContinuous dual spaceLinear functionalRow vectorConjugate transpose
7 related topics

Motivation

AntilinearLinear mapOpposite ringModuleOpposite category
6 related topics

Complex conjugation functor

FunctorCategoryMatrixBases
4 related topics

Structure of the conjugate

DimensionIsomorphicNatural isomorphism
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Complex conjugation functor

Structure of the conjugate

Complex conjugate of a Hilbert space

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Complex conjugate of a vector space

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Avg. degree1.94
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displaystyle complex conjugate overline vector alpha space linear multiplication scalar structure map conjugation functor spaces mathcal cdot antilinear hilbert mathematics

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