Let be a finite dimensional vector space over . Let be a linear transformation
on all of whose eigenvalues are zero. Show that for some , i.e.
that is nilpotent.
Let be a finite dimensional vector space over . Let be a linear transformation
on all of whose eigenvalues are zero. Show that for some , i.e.
that is nilpotent.
Let be a finite dimensional vector space over . Let be a linear transformation
on all of whose eigenvalues are zero. Show that for some , i.e.
that is nilpotent.
Well, then you have it, don't you? If all eigenvalues are 0, then the characteristic equation is and every matrix satisfies its own characteristic equation.