The Plastic dataset is from an industrial experiment found in a textbook by Johnson and Wichern, 1992. Data is also found in R documentation as an example of the function manova.The dependent variables are taken to be "tear","gloss" and "opacity". The independent variables are taken to be "rate" (actually "rate of extrusian" orginally) and "additive". This dataset was segregated by the variable additive into low_additive and high_additive. Then covariance matricies were computed on the dependent variables. The covariance matrix from low_additive was then mutiplied by the inverse of the covariance matrix of high_additive, resulting in a matrix dataset. additive_sigma_eigv is a matrix of eignvalues from that matrix.
Johnson,R.A. and Wichern, D.W. 1992, Applied Multivariate Statistical Analysis
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