As stated in [this][1] question, the maximum rank of covariance matrix is `n-1` where n is sample size and so if the dimension of covariance matrix is equal to the sample size, it would be singular. I can't understand why we substract 1 from the maximum rank of covariance matrix. [1]: http://stats.stackexchange.com/questions/60622/why-is-a-sample-covariance-matrix-singular-when-sample-size-is-less-than-number