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