Bounds on Mahalanobis norms and their applications

Local and global bounds for ratios of norms, and minimal and maximal norms, are constructed for pairs and ensembles of quadratic norms of , with corresponding results for Mahalanobis distance functions. These support envelopes for distributions of certain quadratic forms in Gaussian variates. Applications are noted in the use of quadratic classification rules and in assessing hit probabilities in ballistic systems.