A note on finite determinacy of matrices
Thuy Huong Pham, Pedro Macias Marques

TL;DR
This paper establishes a precise criterion for when a 2x2 matrix over formal power series is finitely determined under a group action involving coordinate changes and invertible matrix multiplications.
Contribution
It provides a necessary and sufficient condition for finite G-determinacy of matrices in the specified algebraic setting.
Findings
Characterization of finite G-determinacy for 2x2 matrices.
Conditions involving group actions and formal power series.
Advances understanding of matrix classification under transformations.
Abstract
In this note, we give a necessary and sufficient condition for a matrix A in M to be finitely G-determined, where M is the ring of 2 x 2 matrices whose entries are formal power series over an infinite field, and G is a group acting on M by change of coordinates together with multiplication by invertible matrices from both sides.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Differential Equations and Dynamical Systems
