http://mathworld.wolfram.com/ComplexPlane.html http://mathworld.wolfram.com/ComplexPlane.html The definition of a vector space says nothing about whether it do

http://mathworld.wolfram.com/ComplexPlane.html http://mathworld.wolfram.com/ComplexPlane.html The definition of a vector space says nothing about whether it does or does not have a multiplication operation defined on it. A vector space having a multiplication operator has additional structure, but is still a vector space. Example: The space of NxN matrices. There are 2 distinct forms of multiplication on this space: between a vector and a scalar (scalar multiplication), and between vectors (matrix multiplication).