2020/11/30 by Michael Thorne, Thorne, Michael
Mathematics · #93D15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:93D15
paper · pdf · doi:10.48550/arxiv.2012.04601
arxiv created 2020/12/17 · arxiv updated 2020/12/18
σ-Stable matrices are introduced and it is shown that the real roots of the polynomials comprising the coefficients of the characteristic polynomial indicate the coefficient sign changes. A proof of Obrechkoff is then used to show that the largest real root from the coefficients is the point of stability when the maximal eigenvalue of the σ-stable matrix is in ℝ. Some implications of the coefficient behaviour for a scaling relation are then discussed.