Several Schur complement inequalities on block Hadamard product

Yıl 2017, Cilt: 5 Sayı: 4, 242 - 247, 01.10.2017

Mustafa Ozel , Ayca Ileri

Öz

The Schur complement theory is very important in many areas such as statistics, matrix analysis, numerical analysis, and control theory. It is a powerful tool to discuss many significant results. This paper deals with the inequalities involving block Hadamard product of positive definite matrices. By using the definition and the properties of block Hadamard product, we obtain useful inequalities on the Schur complement of the block Hadamard product of two positive definite matrices and their inverses. Finally, we give some numerical examples which confirm our theoritical analysis.

Anahtar Kelimeler

Block matrices, block Hadamard product, Schur complement

Kaynakça

• M. Günther, L. Klotz, Schur’s theorem for a block Hadamard product, Linear Algebra and its Applications, 437(2012) 948-956.
• R. A. Horn, R. Mathias, and Y. Nakamura, Inequalilities for Unitarily Invariant Norms and Bilinear Matrix Products, Linear and Multilinear Algebra, 30(1991), 303-314.
• B. Wang, F. Zhang, Trace and eigenvalue inequaities for ordinary and Hadamard products of positive semidefinite Hermitian matrices, SIAM J. Matrix Anal. Appl., 16(1995) 1173-1183.
• F. Zhang, Matrix Theory: Basic results and techniques, Springer, 2011.