In mathematics, the complexification of a vector space over the field of real numbers (a "real vector space") yields a vector space over the complex number field, obtained by formally extending the scaling of vectors by real numbers to include their scaling ("multiplication") by complex numbers. Any basis for (a space over the real numbers) may also serve as a basis for over the complex numbers.
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linear map
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adjoint functor
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mathematics
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International Standard Book Number
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complex number
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matrix
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vector space
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quaternion
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field
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isomorphism
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category theory
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basis
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complex conjugate
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identity function
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octonion
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involution
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Paul Halmos
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dimension of a vector space
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dual space
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linear subspace
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