LDA can be generalized to multiple discriminant analysis, where "c" becomes a categorical variable with "N" possible states, instead of only two. Analogously, if the class-conditional densities formula_65 are normal with shared covariances, the sufficient statistic for formula_66 are the values of "N" projections, which are the subspace spanned by the "N" means, affine projected by the inverse covariance matrix. These projections can be found by solving a generalized eigenvalue problem, where the numerator is the covariance matrix formed by treating the means as the samples, and the denominator is the shared covariance matrix. See “Multiclass LDA” above for details.