/sci/ - Science & Math

>>8990131
>>8990145
>>8990150
The operator norm is sub-multiplicative and the op. norm of a unitary matrix or its inverse is 1. So:
[math] \| [U,V] - I \|_{op} = \| (UV - VU)U^{-1}V^{-1}\|_{op} \leq \| UV - VU \|_{op}=\| (U-I)(V-I) - (V-I)(U-I) \|_{op} \leq 2 \| U-I \|_{op} \| V-I \|_{op} [/math].