矩阵右半张量积的Schur补的奇异值估计

Estimates for Singular Values of Schur Complements of the Right Semitensor Product of Complex Matrices

对矩阵AB的奇异值,特别是最小奇异值的下界估计,是矩阵分析中的重要课题.其有很重要的理论和实际应用价值.主要研究了矩阵右半张量积特征值与(Schur补的)奇异值上(下)界估计,给出了一些Hermite矩阵右半张量积的特征值与奇异值的不等式,并且利用分块矩阵的变换技巧,得到了复杂矩阵右半张量积的Schur补的奇异值估计,改进和推广了一些现有不等式,同时进一步丰富了半张量积的理论知识.

Singular value of the product of matrix AB, in particular the lower bound of the smallest singular value estimate, is an important issue in matrix analysis with important theoretical and practical application value. Some upper （lower） bound estimates for eigenvalues and singular values of Schur complements of right semitensor product of matrix are studied in this paper, some inequalities for eigenvalues and singular values of right semitensor product of Hermite matrix are given, and the singular values of Schur complements of right semitensor product of complex matrices are obtained by using the transformation skills of block matrices. All of these improve and generalize some of the existing inequalities and enrich the semi-tensor product of theoretical knowledge.