Some eigenvalues and trace inequalities for matrices

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Tezin Türü: Yüksek Lisans

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

Tezin Onay Tarihi: 2013

Tezin Dili: İngilizce

Öğrenci: DİLEK VAROL

Danışman: Mustafa Özel

Özet:

ABSTRACT

In matrix theory, the more information about the spectrum gives the power of

understanding matrices better. The spectrum can be identified by the knowledge of

the spectral radius and the minimum eigenvalue of a matrix. In this thesis, the studies

about the lower and upper bounds for the spectral radius and the lower bounds for the

minimum eigenvalue of a matrix are investigated. In these studies, the Hadamard, the

Kronecker and the Fan product of matrices are widely used to establish new types of

matrices. Then several existing results are improved for these products and their

algebraic characterizations. Furthermore, the lower bounds for the minimum

eigenvalue of the Hadamard product of an M-matrix and its inverse are examined and

some new lower bounds are computed.

Keywords: Spectral radius, minimum eigenvalue, inverse of a matrix, Hadamard

product, M-matrix.