Inertia of Kraus matrices

This article is published open access under our Subscribe to Open model.

Abstract

For positive real numbers $r$ , $p_{0}$ , and $p_{1} < \dots < p_{n},$ let $K_{r}$ be the $n \times n$ Kraus matrix whose $(i, j)$ entry is equal to

\frac{1}{p _{i} - p _{j}} (\frac{p _{i}^{r} - p _{0}^{r}}{p _{i} - p _{0}} - \frac{p _{j}^{r} - p _{0}^{r}}{p _{j} - p _{0}}) .

We determine the inertia of this matrix.

Takashi Sano, Kazuki Takeuchi, Inertia of Kraus matrices. J. Spectr. Theory 12 (2022), no. 4, pp. 1443–1457