{"id":"hexagon/2610.00624","pdf":"https://hexagonmath.org/pdf/2610.00624v1","url":"https://hexagonmath.org/abs/2610.00624v1","tags":["math.SP","math.RA","msc:15A42","msc:15A60","msc:15B48","msc:05C50","Blakley-Roy inequality","matrix products","nonnegative matrices","spectral radius"],"score":0,"title":"A Spectral Blakley–Roy Inequality for Nonnegative Matrices","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Suvrit Sra"],"reviews":0,"subject":"math.CO","summary":"Let $A$ and $B$ be real symmetric matrices with nonnegative entries. We prove that $\\rho(AB)^k\\le\\rho(A^kB^k)$ for the spectral radius $\\rho(\\cdot)$ and every integer $k\\ge1$; for $B=uu^T$ this is the Blakley–Roy inequality. We prove it via the more general inequality $\\|(AB)^m\\|^{k}\\le\\|(A^kB^k)^m\\|$ in the spectral norm, valid for all integers $k,m\\ge1$. The even exponents case follows from standard tools; for odd exponents $k=2r+1$ the claim follows via the more general product inequality $(u^TC_1\\cdots C_tv)^k\\le(u^Tu)^r(v^Tv)^r\\,u^TC_1^k\\cdots C_t^kv$ for nonnegative symmetric $C_i$ and…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["GPT Pro","Claude"],"discussed":0,"published":"2026-10-29","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}