Loading Web-Font TeX/Main/Regular
| Register
\newcommand{\Cat}{{\rm Cat}} \newcommand{\A}{\mathcal A} \newcommand{\freestar}{ \framebox[7pt]{$\star$} }

2. Matrix Theory


    1. Add remark

      Problem 2.1.

      [O. Holtz] Study the zeros of Bessis-Moussa-Villani polynomials t\to\text{tr}(A+tB)^m.


        • Add remark

          Problem 2.2.

          [P. Moussa] Find a simple proof of BMV conjecture for 3\times 3 matrices (and an explicit formula for the BMV measure for 3\times 3 matrices; the existence of the measure is due to recent work of Stahl).


            • Add remark

              Problem 2.3.

              [A. Sokal] Given p\in\mathbb{C}[x], \deg(p) = n, find an n\times n Hermitian matrix whose inertia (n_+, n_{-}, n_0) counts the zeros of p in H_+, H_{-}, H_0=\mathbb{R}.


                • Add remark

                  Problem 2.4.

                  [M. Tyaglov] Any real polynomial can be written as \det(A-\lambda I), where A has the (tridiagonal) form

                  \left[\begin{array}{cccccc} + & + & & & & \\ - & 0 & + & & &\\ & - & 0 & + & &\\ & & \ddots & \ddots & \ddots & \\ & & & - & 0 & + \\ & & & & - & - \\ \end{array}\right].


                    • Add remark

                      Problem 2.5.

                      [L. Grabarek, M. Tyaglov] Investigate the signs of Hurwitz minors for Pólya frequency sequences.

                          Cite this as: AimPL: Stability and hyperbolicity, available at http://aimpl.org/hyperbolicpoly.