this problem is about abstract algebra, especially is group theory.
Let G=GL2(C). which means general linear group with each components are complex number.
and let H = {2x2 matrix (a b ; c d) l a,b,c are in Complex number, ac is not zero}
Prove that every element of G is conjugate to some element of the subgroup H and deduce that G is the union of conjugates of H [ Show that every element of GL2(C) has an eigenvector ]
This problem is about abstract algebra, especially is group theory. Let G=GL2(C). which means gen...