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Complexification
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In mathematics, the complexification of a vector space V over the real number field is the 'corresponding' vector space VC over the complex number field. That is, it shares the same dimension as V; and a basis for V over the real numbers can serve as a basis for VC over the complex numbers.
For example, if V consists of the m×n matrices with real coefficients, VC would consist of m×n complex matrices.
For the sake of having a basis-free definition, one can take
,
the tensor product over the real field of V and the complex numbers.
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details