The decomposition solvers can "invert" non-square matrices. There is no documentation describing what exactly is being returned in these cases. It is not obvious to me exactly what conditions the returned value satisfies in each case when the actual parameter is not square. Do all of them return pseudo-inverses X satisfying AXA = A where A is the input matrix? Do they satisfy other conditions as well? Under what conditions will exceptions be thrown? We should either throw NonSquareMatrixException (as MatrixUtils now does) on non-square arguments or define precisely what is being computed by each of the solvers for non-square arguments and what the preconditions are.
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