Exercise:

Prove that if X and Y are in little o n then X bracket Y is also in little o n.

Exercise:

Prove that if X and Y are in little o n then X bracket Y is also in little o n.

Exercise:

Show that X equals 0, 1; 0, 0 and Y equals 0, 0; 1, 0 are in little s l 2 C.

Exercise:

Check that the Jacobi identity holds for the commutator bracket X bracket Y equals X Y minus Y X.

Exercise:

Why is the tangent vector to exp of s X at s = 0 equal to X?