超定、适定、欠定

AX = B (1)
To begin with, we suppose that A is full-rank.
If $A\in R^{n\times m},n>m,X\in R^m,B \in R^n$,equation (1) is a overdetermined equation ;
if $n<m$, then it is a underdetermined equation;
otherwise ,$n = m$,that is a well-posed equation.
in the first case, the number of equations is larger than the number of unknown variables ,in other words ,the conditions is too strict that we may cannot find a solution that suit all the conditions, generally speaking, we use least-squares to solve this problem.
in the second case, the number of equations is smaller than the number of unknown variables, interior point method and gradient projection methord is commonly used to solve underdetermined equation.
in the third case, you know, I need not to say more!