Theoretical Statistics and Mathematics Unit, ISI 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.