Equation 12.6.138B3AE102E667

\begin{align} d_ W(A,B)& \geq \frac1{\sqrt n} \| \log (A^{-1/2}BA^{-1/2})\| _{\mathrm F},\\ d_ W(A,B)& \leq \frac{\| A-B\| _{\mathrm F}}{\sqrt n\min \{ \lambda _{\min }(A),\lambda _{\min }(B)\} }. \tag{12.6.14} \end{align}