The fundamental example of a linear complex structure is the structure on R2"n" coming from the complex structure on C"n". That is, the complex "n"-dimensional space C"n" is also a real 2"n"-dimensional space – using the same vector addition and real scalar multiplication – while multiplication by the complex number "i" is not only a "complex" linear transform of the space, thought of as a complex vector space, but also a "real" linear transform of the space, thought of as a real vector space. Concretely, this is because scalar multiplication by "i" commutes with scalar multiplication by real numbers formula_7 – and distributes across vector addition. As a complex "n"×"n" matrix, this is simply the scalar matrix with "i" on the diagonal. The corresponding real 2"n"×2"n" matrix is denoted "J".