  In this paper, the singular-value decomposition theory of complex matrices is
explored to study constantly curved 2-spheres minimal in both $\mathbb{C}P^n$
and the hyperquadric of $\mathbb{C}P^n$. The moduli space of all those
noncongruent ones is introduced, which can be described by certain complex
symmetric matrices modulo an appropriate group action. Using this description,
many examples, such as constantly curved holomorphic 2-spheres of higher
degree, nonhomogenous minimal 2-spheres of constant curvature, etc., are
constructed. Uniqueness is proven for the totally real constantly curved
2-sphere minimal in both the hyperquadric and $\mathbb{C}P^n$.
