Abstract <p>Dimension reduction is an important, often essential, component of multivariate analysis. It is usually an intermediary step to make the multivariate inference of interest meaningful. In classification, for example, it helps determine the subset of features that significantly contribute to classification, in order to enhance the optimality of the classifier. The present article addresses this issue by modifying a classical test to determine the feature subspace which may be discarded as redundant to enable the remaining, potentially contributing, features to improve the classifier. The proposed test allows the dimension, also of sub-vectors, to exceed the sample sizes. The test is constructed under a general multivariate model, with normality as a special case, and a few mild assumptions. Two-class case is discussed in detail, with a brief extension to multi-class case. Simulations are used to demonstrate the accuracy of the proposed theory, and its applications are illustrated through several real data examples.</p>