Given a matrix equation
the normal equation is that which minimizes the sum of the square differences between the left and right sides:
It is called a normal equation because 
is normal to the range of 
.
Here, 
is a normal matrix.
See also
Least Squares Fitting, Moore-Penrose Matrix Inverse, Nonlinear Least Squares Fitting, Normal Matrix, Pseudoinverse
Explore with Wolfram|Alpha
More things to try:
Cite this as:
Weisstein, Eric W. "Normal Equation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NormalEquation.html