In this paper, by using the Moore-Penrose generalized inverse of the covariance matrix, for the mean-variance selection problem of any finite kinds of risk assets portfolio, the expression of the optimal strategies and the variance for the minimum variance portfolio under the given portfolio expected return are given. By proceeding the generalized inverse analysis, we further deduced the geometric characterization of the efficient frontier of the portfolio under two different circumstances, respectively. The conclusions not only include the results of the covariance matrix under the positive definite condition in the literature, but also include the classical results of the geometric characterization of the effective frontier of the portfolio when $n=2$ and the two risky assets are completely negatively correlated.