Let me talk about a concept:
Overdetermined equation : When m of A (mx n) in AX = b is greater than n, this equation is an overdetermined equation. There is a possibility that the overdetermined equation has no solution, so we encounter overdetermined equations (and other types of When the equation may have no solution), it is generally to find its least square solution (that is, let ||AX-b|| the smallest X).
According to blog post 1 , there are many kinds of least squares solutions to equations.
According to this PPT , the most commonly used least squares solution is one, which is the second (normal equation) in the blog post, that is: if the equation is AX = b, then the least squares solution is .
However, to apply the least squares solution, there is a prerequisite, that is, it must be reversible. To be
reversible, that is, the rank of A must be equal to the number of columns.