is paper, using tra~sfo~atio~ of Schr estimates of eigenvnlues of positive se~~i~efiuite ualities of singular values for Schur co tian matrices we Kevwor&~ . .
Some inequalities for Schur complements
โ Scribed by Jianzhou Liu; Jian Wang
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 93 KB
- Volume
- 293
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
โฆ Synopsis
We shall obtain some inequalities for Schur complements of products and sums of matrices.
๐ SIMILAR VOLUMES
This paper presents some inequalities on generalized Schur complements. Let A be an n ร n (Hermitian) positive semideยฎnite matrix. Denote by eaa the generalized Schur complement of a principal submatrix indexed by a set a in A. Let e be the Mooreยฑ Penrose inverse of A and ke be the eigenvalue vector
Suppose A and B are n ร n matrices over the complex field. An inequality is derived that relates the Schur complement of the Hadamard product of A and B and the Hadamard product of Schur complements of A and B for positive definite matrices. Then an analog is given for the class of tridiagonal total
Let A โ R n,n and let ฮฑ and ฮฒ be nonempty complementary subsets of {1, . . . , n} of increasing integers. For ฮป > ฯ(A[ฮฒ]), we define the generalized Perron complement of A[ฮฒ] in A at ฮป as the matrix For the classes of the nonnegative matrices and of the positive semidefinite matrices, we study the