A point of an algebraic variety which is not singular is said to be regular. An algebraic variety which has no singular point is said to be non singular or smooth.For example, the plane algebraic curve (a cubic curve) of equationy2 - x2(x + 1) = 0,
A linear mapping is a mapping that "preserves" the two basic operations of a vector space, that of vector addition and that of scalar multiplication. A linear mapping effects a vector space homomorphism. If it is nonsingular it effects a vector space isomorphism. A consequence of the linearity of a mapping is that subspaces are mapped into subspaces.
          eg:   Vn(F), is
                  y = Ax