I am getting all singular matrices in my research on the quantization of one-dimensional space. I think this is the proper place for me to ask all mathematicians the disadvantage of singular matrix. I know that singular matrix does not have an inverse since its determinant is zero and hence a metric cannot be defined. What is the parctical use of a metric besides giving a "distance?" Zero metric can also mean zero mass in physics. But if all masses are zeros, where do the experimentally determined masses come from?