On some mean matrix inequalities of dynamical interest
| dc.creator | Rivin, Igor | |
| dc.date | 2003-12-02 | |
| dc.date | 2003-12-11 | |
| dc.date.accessioned | 2026-07-07T05:03:28Z | |
| dc.date.available | 2026-07-07T05:03:28Z | |
| dc.description | Let A be an n by n matrix with determinant 1. We show that for all n > 2 there exist dimensional strictly positive constants C_n such that the average over the orthogonal group of log rho(A X) d X > C_n log ||A||, where ||A|| denotes the operator norm of A (which equals the largest singular value of A), rho denotes the spectral radius, and the integral is with respect to the Haar measure on O_n The same result (with essentially the same proof) holds for the unitary group U_n in place of the orthogonal group. The result does not hold in dimension 2. We also give a simple proof that the average value over the unit sphere of log ||A u|| is nonnegative, and vanishes only when A is orthogonal. | |
| dc.description | 11 pages; revision shows notes that it is essentially necessary to use Haar measure (class) | |
| dc.identifier | https://arxiv.org/abs/math/0312048 | |
| dc.identifier | http://arxiv.org/abs/math/0312048 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69428 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Functional Analysis | |
| dc.subject | 37D25;37A25; 15A45; 15A52 | |
| dc.title | On some mean matrix inequalities of dynamical interest | |
| dc.type | text |