论文信息 - Some Properties of Symmetric Quasi-Definite Matrices

Some Properties of Symmetric Quasi-Definite Matrices

Symmetric quasi-definite matrices arise in numerous applications, notably in interior point methods in mathematical programming. Several authors have derived various properties of these matrices. This article provides a list of some previously known properties and adds a number of others that are believed to be new.

[1] Gene H. Golub,et al. Matrix computations , 1983 .

[2] Joseph R. Shinnerl,et al. On the Stability of Cholesky Factorization for Symmetric Quasidefinite Systems , 1996, SIAM J. Matrix Anal. Appl..

[3] Robert J. Vanderbei,et al. Symmetric Quasidefinite Matrices , 1995, SIAM J. Optim..

[4] Charles R. Johnson,et al. Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[5] Robert C. Thompson. The eigenvalues of a partitioned Hermitian matrix involving a parameter , 1974 .

[6] G. Stewart. Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems , 1973 .

[7] H.P.M. v. Kempen. Variation of the eigenvalues of a special class of hermitian matrices upon variation of some of its elements , 1970 .