Inequalities of block matrices in the context of the schur complement

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Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Dokuz Eylül Üniversitesi, Fen Bilimleri Enstitüsü, MATEMATİK, Türkiye

Tezin Onay Tarihi: 2015

Tezin Dili: İngilizce

Öğrenci: AYÇA İLERİ

Danışman: Mustafa Özel

Özet:

ABSTRACT

Schur complement is a key tool in many areas of matrix analysis and a rich source for matrix inequalities. The use of the Schur complement technique has an algorithmic structure in calculating matrix inverses and linear systems. In this study we examine equalities and inequalities involving the Schur complement of the large sized matrices. For this purpose we use positive definite and positive semi definite block matrices and examine the Schur complement of their products, such as Hadamard product, Kronecker product. Also in this thesis we analyze the block form of Hadamard and Kronecker products. We make an analogy between the inequalities involving Hadarmard, Kronecker products and block form of these products.

Keywords: Schur complement, Hadamard product, Kronecker product, block Hadamard product, block Kronecker product