asset portfolio;  mean-variance criterion;  Matrix

The Lagrange solution method of the mean-variance criterion of portfolio theory is analyzed, and it is pointed out that since the Lagrange method only gives the necessary conditions for the existence of extreme points, the solution method is used to prove that there is a defect in the existence of the portfolio with the smallest variance at a certain time of return. Taking the matrix as the analysis tool, the restriction condition is expressed in the form of a generalized inverse matrix of the solution of the linear equation system, and a new solution to the mean-variance criterion is given through the theory of the solution of the linear equation system.