In certain multivariate problems involving several populations, the covariance structure of the populations is such that all covariance matrices can be diagonalized simultaneously by a fixed orthogonal transformation. In the transformed problem one has a number of independent univariate populations. Consequently certain hypotheses in the original problem become equivalent to simultaneous hypotheses on these univariate populations in the transformed model. Using this approach we propose a test procedure for testing the hypothesis of equality of covariance matrices against a certain alternative under the intraclass correlation model. The relative advantages of our procedure over that of Srivastava's procedure  are also discussed. Finally we indicate how the problem of testing for the equality of covariance matrices under a more general set up can be reduced to a univariate problem.
"Tests for the Equality of Covariance Matrices under the Intraclass Correlation Model." Ann. Math. Statist. 38 (4) 1286 - 1288, August, 1967. https://doi.org/10.1214/aoms/1177698801