Proving the Uncertainty Relation for Finite Dimensional Hermitian Matrices

[yukawa]

Show that [A,B] = AB - BA = iqI, where q is a real no. and I is the identity matrix, cannot be satisfied by any finite dimensional Hermitian matrix A and B.


I think this problem is something related to the uncertainity relation:
$$<(\Delta A)^{2}><(\Delta B)^{2}>\geq \frac{\left|C\right| ^{2}}{4}$$
but I don't know how to find the variance of A and B ...

How should I approch this problem? Are there any trick to do with the "finite dimension" ?

 

[borgwal]

No, the problem has nothing to do with the uncertainty relations. Try taking the trace of both left-hand and right-hand sides of your equation.