‘An inequality with application to multivariate analysis’

Abstract

I am grateful to Professor W. Kristof for pointing out two errors in my paper. In the Corollary to Theorem 1, D should be definite, and in Theorem 2, D + U should be definite. These conditions are satisfied in the applications given. The inequality of Theorem 1 is similar to a result presented by von Neumann (1937). Kristof (1970) gives a generalization of this and some applications in psychometrics. On page 466, line 13 should read Θ ^ = ( N T ) 1 [ diag { Φ 1 ( T ) , … , Φ r ( T ) } / k - I r ] ( N ′ T ) 1 The additional references are: KRISTOF, W. (1970). A theorem on the trace of certain matrix products and some applications. J.Math. Psychol . 7, 515–30. VON NEUMANN, J. (1937). Some matrix inequalities and metrization of matric-space. Tomsk Univ. Rev . 1, 286–300. Reprinted in A.H. Taub (Ed.) (1962). John von Neumann: Collected Works , Vol. 4. New York: Pergamon.