# Seminar at SMU Delhi

April 9, 2014 (Wednesday) , 3:30 PM at Webinar
Speaker: Tanvi Jain, Indian Statistical Institute, Delhi
Title: Spectra of some special matrices
Abstract of Talk
Let $p_1,\ldots,p_n$ be distinct positive real numbers and let $r>0$. The $n\times n$ matrix $C=[(p_i+p_j)^{-1}]$ is called Cauchy matrix, the special case being the well-known Hilbert matrix when each $p_i=i$. It is known that $C$ is positive definite. More generally, the matrix $C^{\circ r}=[(p_i+p_j)^{-r}]$ is positive definite. On the otherhand the study of spectra of matrices $[(p_i+p_j)^r]$ reveals a very interesting behaviour. The focus of this talk is to investigate inertias of these matrices.