SCHUR COMPLEMENTS OF BLOCK KRONECKER PRODUCTS

Öz

The paper is established on Schur complements and block Kronecker product of positive semidefinite matrices. In particular, a formulation for the block Kronecker product of Schur complements of block matrices is improved. Additionally, an new following inequality for block Kronecker product of Schur complements of two matrices and their conjugate transpose is proved

Anahtar Kelimeler

• Schur Complements, Block Kronecker Product, Positive Semidefinite Matrices, MoorePenrose Inverse

BLOK KRONECKER ÇARPIMLARIN SCHUR TAMAMLAYICILARI

Öz

Bu çalışma, yarı pozitif tanımlı blok matrislerin blok kronecker çarpımları ve Schur tamamlayıcıları üzerine kurulmuştur. Özellikle blok matrislerin Schur tamamlayıcılarının blok kronecker çarpımı için bir formülasyon geliştirilmiştir. Bundan başka, iki matris ve eşlenik transpozlarının schur tamamlayıcılarının blok kronecker çarpımları için aşağıdaki yeni eşitsizlik kanıtlanmıştır

Anahtar Kelimeler

• Schur Tamamlayıcılar, Blok Kronecker Çarpım, Yarı Pozitif Tanımlı Matrices , Moore-Penrose Tersler

Kaynakça

1. Brewer, J.W. 1978 Kronecker products and matrix calculus in system theory, IEEE Transactions on Circuits and Systems, Vol. Cas- 25, No.9.
2. Horn, R.A., Mathias, R., and Nakamura, Y. 1991. Inequalities for unitarily invariant norms and bilinear matrix products, Linear and Multilinear Algebra, 30, 303- 314.
3. Günther, M. & Klotz, L. 2012. Schur’s theorem for a block Hadamard product, Linear Algebra and its Applications, 437, 948-956.
4. Horn, R. A. & Johnson, C.R. 2013. Matrix Analysis, Cambridge University Press, New York.
5. Liu, J. 1999. Some Löwner partial orders of Schur complements and Kronecker products of matrices, Linear Algebra and its Applications, 291, 143-149.
6. Zhang, F. 2005. The Schur complement and its applications, Vol. 4, Springer Science & Business Media.
7. Albert, A. 1969. Conditions for positive and nonnegative definiteness in terms of pseudoinverses, SIAM J. Appl. Math. 17, 434-440.