Normal forms of endomorphism-valued power series

2016/10/26 by Keane, Christopher, Szabó, Szilárd · 1 citation
#05E40 #15A21 #15A54 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1610.08485

Abstract

We show for n,k≥1, and an n-dimensional complex vector space V that if an element A\inEnd(V)[[z]] has constant term similar to a Jordan block, then there exists a polynomial gauge transformation g such that the first k coefficients of gAg^-1 have a controlled normal form. Furthermore, we show that this normal form is unique by demonstrating explicit relationships between the first nk coefficients of the Puiseux series expansion of the eigenvalues of A and the entries of the first k coefficients of gAg^-1.

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