A criterion of simultaneously symmetrization and spectral finiteness for a finite set of real 2-by-2 matrices
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In this paper, we consider the simultaneously symmetrization and spectral finiteness for a finite set of real 2-by-2 matrices.
💡 Research Summary
The paper addresses two intertwined problems for a finite collection of real 2 × 2 matrices 𝔄 = {A₁,…,Aₖ}: (1) when can all matrices be simultaneously symmetrized by a single similarity transformation, and (2) under what conditions does the joint spectral radius (JSR) of 𝔄 attain its value on a finite product of the matrices (spectral finiteness).
The authors first write each matrix as
Aᵢ =
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