2.17 ( ) www Consider the multivariate Gaussian distribution given by (2.43). By writing the precision matrix (inverse covariance matrix) 1 as the sum of

2.17 () www Consider the multivariate Gaussian distribution given by (2.43). By writing the precision matrix (inverse covariance matrix) Σ−1 as the sum of a symmetric and an anti-symmetric matrix, show that the anti-symmetric term does not appear in the exponent of the Gaussian, and hence that the precision matrix may be taken to be symmetric without loss of generality. Because the inverse of a symmetric matrix is also symmetric (see Exercise 2.22), it follows that the covariance matrix may also be chosen to be symmetric without loss of generality.