  To explore the limits of a stochastic gradient method, it may be useful to
consider an example consisting of an infinite number of quadratic functions. In
this context, it is appropriate to determine the expected value and the
covariance matrix of the stochastic noise, i.e. the difference of the true
gradient and the approximated gradient generated from a finite sample. When
specifying the covariance matrix, the expected value of a quadratic form QBQ is
needed, where Q is a Wishart distributed random matrix and B is an arbitrary
fixed symmetric matrix. After deriving an expression for E(QBQ) and considering
some special cases, a numerical example is used to show how these results can
support the comparison of two stochastic methods.
