In Bishop's *Pattern Recognition and Machine Learning*, he states on page 80 in reference to the squared Mahalanobis distance $(\mathbf{x} - \boldsymbol{\mu})^\top\boldsymbol{\Sigma}^{-1}(\mathbf{x} - \boldsymbol{\mu})$ that: 

> 
> the matrix $\boldsymbol{\Sigma}$ can be taken to be symmetric,
>  without loss of generality, because any antisymmetric component would
>  disappear from the exponent.
> 
> 
> 

My understanding was that all covariance matrices must be symmetric, so could someone please explain what this statement means?