A matrix inequality on Schur complements
โ Scribed by Zhong-Peng Yang; Chong-Guang Cao; Xian Zhang
- Book ID
- 105663106
- Publisher
- Springer-Verlag
- Year
- 2005
- Tongue
- English
- Weight
- 140 KB
- Volume
- 18
- Category
- Article
- ISSN
- 1598-5865
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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
We shall obtain some inequalities for Schur complements of products and sums of matrices.
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