# Gersgorin’s theorem for estimating eigenvalues.

Speaker : Soumitra Ghara

Date : 19th August, 2014 (Tuesday)

Time : 09:15 pm – 10:15 pm

Venue : Lecture Hall I, Department of Mathematics

Abstract: In this talk we prove that all eigenvalues of a square matrix $(a_{ij})_{1 \le i,j \le n}$ lie in the union of disks $\{z ; | z-a_{ii}| \leq \Sigma_{j=1 , j \neq i} ^ n |a_{ij}| \}$. As an application we will prove that strictly diagonally dominated matrices are nonsingular. We will also see some consequences of the above theorem.

Area: Linear Algebra