一类实矩阵对广义奇异值的表达公式

The Formula of Generalized Singular Values of a Class of Real Matrix Pairs

摘要: 应用双随机矩阵的性质, 首先得到了一类实对角矩阵迹函数优化问题的解析解, 再由该解析解得到了计算实矩阵对第i个广义奇异值的表达公式, 最后数值算例验证了结论的有效性.

Abstract: Using the properties of doubly stochastic matrices, the analytic solutions to a class of real diagonal matrix optimization problems are obtained, and then the formula for the i-th generalized singular value of a real matrix pair is obtained from the analytic solutions. Finally, numerical examples verify the validity of the conclusion.