We study the average condition number for polynomial eigenvalues of collections of matrices drawn from some random matrix ensembles. In particular, we prove that polynomial eigenvalue problems defined by matrices with random Gaussian entries are very well conditioned on the average.

UR - https://doi.org/10.1007/s10208-019-09414-2 ER - TY - JOUR T1 - On fully real eigenconfigurations of tensors JF - SIAM Journal on Applied Algebra and Geometry Y1 - 2018 A1 - Khazhgali Kozhasov AB -We construct generic real symmetric tensors with only real eigenvectors or, equivalently, real homogeneous polynomials with the maximum possible finite number of critical points on the sphere.

PB - SIAM VL - 2 UR - https://epubs.siam.org/doi/pdf/10.1137/17M1145902 ER - TY - RPRT T1 - Random spectrahedra Y1 - 2017 A1 - Paul Breiding A1 - Khazhgali Kozhasov A1 - Antonio Lerario ER -