Journal of Prime Research in Mathematics

# Determinant Spectrum of Diagonal Block Matrix

Elif OTKUN CEVIK$$^{a,*}$$, Zameddin I. ISMAILOV$$^b$$
$$^a$$Department of Mathematics, Avrasya University, Trabzon, Turkey.
$$^b$$Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey.
Correspondence should be addressed to: Elif OTKUN EVIK at elifotkuncevik@gmail.com

### Abstract

It is known that in mathematical literature one of important questions of spectral theory of operators is to describe spectrum of diagonal block matrices in the direct sum of Banach spaces with the spectrums of their coordinate operators. This problem has been investigated in works [1] and [2]. Also for the singular numbers similar investigation has been made in [3]. In this paper the analogous question is researched. Namely, the relationships between $$\epsilon$$-determinat spectrums of the diagonal block matrices and their block matrices are investigated. Later on, some applications are given.

#### Keywords:

Eigenvalues, Spectrum, Determinant, Diagonal Block Matrix.