1. A method for determining ill conditioning in square linear systems of equations, the method comprising: sampling, by a processor, a plurality of condition numbers in the square linear systems of equations; classifying the condition numbers sampled from the square linear systems of equations in different categories; generating statistics information on the square linear systems of equations for each of the different categories of the classifying; and displaying the statistics information and the different categories according to classification of each of the plurality of condition numbers on a display and, depending on a value of the statistics information, displaying notification that the square linear systems of equations are ill conditioned.