A curve (or geometric object more generally) is non-singular if it has no singular points. So a parabola is non-singular, but the curve with equation y2 = x3 is not, having a singular point (a cusp) at the origin.
A square matrix A is non-singular if it is not singular; that is, if detA ≠ 0, where detA is the determinant of A. See alsoinverse matrix.