A complex vector space is a vector space whose field of scalars is the complex numbers. A linear transformation between complex vector spaces is given by a matrix with complex entries (i.e., a complex matrix).
Complex Vector Space
See also
Complex Structure, Linear Transformation, Real Vector Space, Vector Basis, Vector SpaceThis entry contributed by Todd Rowland
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Rowland, Todd. "Complex Vector Space." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ComplexVectorSpace.html