Complex projective line

As the complex projective line

The Riemann sphere can also be defined as the complex projective line. The points of the complex projective line can be defined as equivalence classes of non-null vectors in the complex vector space ${\displaystyle \mathbf {C} ^{2}}$: two non-null vectors ${\displaystyle (w,z)}$ and ${\displaystyle (u,v)}$ are equivalent iff ${\displaystyle (w,z)=(\lambda u,\lambda v)}$ for some non-zero coefficient ${\displaystyle \lambda \in \mathbf {C} }$.