TOPICS
Search

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, Pseudoinverse

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Normal Equation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NormalEquation.html

Subject classifications