Wei Xie

Negative inertia of entrywise powers

For $\alpha>0$, let $M_n(\alpha)$ be the largest possible number ofnegative eigenvalues of $A^{\circ\alpha}$, where $A$ ranges over the realpositive definite matrices of order $n$ with strictly positive entries.For $n\geq3$, we prove\[ M_n(\alpha)=n-2 \qquad\left(0<\alpha<\frac1{...