On the real Davies' conjecture

Vishesh Jain, Ashwin Sah, Mehtaab Sawhney

We show that every matrix $A\in {\mathbb{R}}^{n\times n}$ is at least $\delta$$\Vert A\Vert$-close to a real matrix $A+E\in {\mathbb{R}}^{n\times n}$ whose eigenvectors have condition number at…