Normal Equation

Given an overdetermined Matrix Equation

$${\hbox{\sf A}}{\bf x}={\bf b},$$

the normal equation is that which minimizes the sum of the square differences between left and right sides

$${\hbox{\sf A}}^{\rm T}{\hbox{\sf A}}{\bf x}={\hbox{\sf A}}^{\rm T}{\bf b}.$$

See also Least Squares Fitting, Moore-Penrose Generalized Matrix Inverse, Nonlinear Least Squares Fitting