关于半正定矩阵的若干结果Some results related to positive semidefinite matrices
夏顺友,曾诚
摘要(Abstract):
利用分块矩阵和Schur补得到了关于半正定矩阵Moore-Penrose逆的若干矩阵等式和矩阵不等式,相应地推广了某些已知结果.
关键词(KeyWords): Schur补;半正定矩阵;Moore-Penrose逆;矩阵等式;矩阵不等式
基金项目(Foundation): 国家自然科学基金资助项目(11161008);; 贵州省科技基金资助项目(2012GZ71164)
作者(Author): 夏顺友,曾诚
DOI: 10.13391/j.cnki.issn.1674-7798.2013.06.004
参考文献(References):
- [1]R A Horn,C R Johnson.Matrix Analysis[M].Cam-bridge University Press,New York,1985.
- [2]B Wang,F Zhang.Schur complements and matrix ine-qualities of Hadamard products[J].Linear and Multilin-ear Algebra,1997,43:315-326.
- [3]F Zhang.Matrix Theory:Basic Results and Techniques[M].Springer,New York,1999.
- [4]F Zhang.Schur complements and matrix inequalities inthe Lowner ordering[J].Linear Algebra and its Applica-tions,2000,321:399-410.
- [5]S Liu.Inequalities Involving Hadamard Products of Posi-tive Semidefinite Matrices[J].Journal of MathematicalAnalysis and Applications,2000,243:458-463.
- [6]B Wang,X Zhang,F Zhang.Some inequalities on gen-eralized Schur complements[J].Linear Algebra Appl.1999,302-303:163-172.
- [7]F Zhang.Matrix Theory:Basic Results and Techniques[M].Springer,New York,1999.
- [8]F Zhang.A matrix identity on the Schur complement[J].Linear and Multilinear Algebra,2004,52:367-373.