“…In high-dimensional data, for one population when the data has the number of variable exceed sample size (minus 1), p > n i -1, for example the data that collects from DNA microarrays technology where a large number of gene expression levels may be in the hundreds or thousands, are measured on relatively few subjects (Zhou et al, 2017), then the sample covariance matrix S i lose its full rank and will be singular, which makes S i does not have an inverse (Chongcharoen, 2011). Furthermore, for two populations when the data has the number of variable is larger than the sum of the sample sizes (minus 2), p > n 1 + n 2 -2, then the sample covariance matrix S ɶ in (7) does not have an inverse.…”