Why is it possible to take the cross product in only 3 and 7 dimensions?
PLease could you elaborate on why determinants of matrices can explain the (non-) existence of smooth (no-where zero, I imagine) vector fields on S^n?Well, the idea is that a matrix is created. The determinent can do very funny things. Just try to find the determinents of 3x3, 4x4, 5x5, 6x6, 7x7. You may figure out why...