RealVectorSpace.md (603B)
1 # Real Vector Space 2 3 **Source:** Linear Algebra Done Right 4 5 **Chapter:** 1 6 7 **Definition:** A real vector space is a [Vector Space](VectorSpace.md) on $R$ where $R$ is the set of real numbers. 8 9 ## Importance 10 11 The importance of this distinction lies in the fact that vector spaces are defined on a set $F$ which is often the set of complex numbers or real numbers, but if we define a set {2,3}, we notice normal vector spaces cease to be so because there is no longer a multiplicative identity. 12 13 In line with this, we also define a complex vector space as a vector space over the set of complex numbers.