According to Wikipedia, the Gauss-Seidel Iteration for solving a linear system of equations Ax=b converges if

A is symmetric positive-definite, or

A is strictly or irreducibly diagonally dominant.

Does this also hold for the Projected Gauss-Seidel (which simply makes the iterate non-negative by taking max(gauss-Seidel iterate,0)?

Similarly, does the convergence criterion for Jacobi iteration also hold for the Projected Jacobi?