Some remarks on the Jordan-Chevalley decomposition
Alberto Dolcetti, Donato Pertici
TL;DR
This paper explores a refined version of the Jordan-Chevalley decomposition of matrices, focusing on the field of coefficients and introducing additional additive and multiplicative decompositions under certain conditions.
Contribution
It provides a detailed study of the fine Jordan-Chevalley decomposition and introduces new additive and multiplicative matrix decompositions based on coefficient fields.
Findings
Refined understanding of the fine Jordan-Chevalley decomposition
New additive decompositions of matrices
New multiplicative decompositions of matrices
Abstract
In this note we mainly study the fine Jordan-Chevalley decomposition: a refinement of the classical Jordan-Chevalley decomposition of a matrix and we pay a particular attention to the field of the coefficients of the matrix. Moreover we obtain some further additive and multiplicative decompositions of a matrix under suitable conditions.
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