For a normal random matrix Y with mean zero, necessary and sufficient conditions are obtained for Y'WkY to be Wishart-Laplace distributed and {Y'WkY} to be independent, where each Wk is assumed to be symmetric rather than nonnegative definite.

For a normally distributed random matrix Y with mean zero and general covariance matrix [Sigma]Y and for a symmetric matrix W, necessary and sufficient conditions are derived for the Wishartness of Y'WY.

Let E, V be n-, p-dimensional inner product spaces over the real field, let (V, E) be the set of all linear maps of V into E, and let Y be a normal random vector in (V, E) with mean [mu] = 0 and covariance [Sigma]Y such that S1 [square not subset] S2([not equal to] }0{) is the image set, Im...