There are several methods known for solving a linear equation system Ax = b (like Jacobi or Gauss-Seidel) by iterating
$x_{n+1}=Mx_n+c$ with a matrix M, for which some norm is smaller than 1. But what can be done if we have an arbitary matrix A with no special properties (not symmetric and not diagonaldominant) ? Must the numerical gauss-algorithm be used, or is there a fix-point-iteration converging in any case ?
A linear equation system $Ax=b$ with arbritray $A$ isn't solvable; just imagine $A_{i,j}=0$ everywhere; you will at least have to assume that the system is solvable aka that $A$ has full rank.
In this case, amongst all iterative methods, GMRES makes the least assumptions. The system doesn't have to be definite or symmetric.