  Perusal of research articles that deal with the topic of matrix calculus
reveal two different approaches to calculation of the gradient of a real-valued
function of a symmetric matrix leading to two different results. In the
mechanics and physics communities, the gradient is calculated using the
definition of a \frechet derivative, irrespective of whether the argument is
symmetric or not. However, members of the statistics, economics, and electrical
engineering communities use another notion of the gradient that explicitly
takes into account the symmetry of the matrix, and this "symmetric gradient"
$G_s$ is reported to be related to the gradient $G$ computed from the \frechet
derivative with respect to a general matrix as $G_s = G + G^T - G \circ I$,
where $\circ$ denotes the elementwise Hadamard product of the two matrices. We
demonstrate that this relation is incorrect, and reconcile both these
viewpoints by proving that $G_s = \mathrm{sym}(G)$.
