Etgen and Pawlowski have recently given criteria for oscillation of matrix differential equations which involve the value of positive linear functional on the matrices appearing in a matrix differential equation. We characterize these functional and indicate relationships to eigenvalue criteria for oscillation. Our results are also useful for the detection of the oscillation of particular matrix differential equations. 1. Introduction. In this article we examine positive linear functionals on

more »

... e linear space of square matrices of order n. We show that there is a one-to-one correspondence between nonnegative definite matrices and positive linear functionals and we bound the value of the positive linear functional on a given matrix by the eigenvalues of the given matrix. These results are useful for the detection of the oscillation of matrix differential equations and we discuss this application in §4 of this article.