The Chevalley--Jordan decomposition and spectral projections of complex matrices

Résumé

In this paper, a novel and simple method for obtaining the Chevalley-Jordan decomposition and the spectral projections
of matrices is presented. Our method is direct and elementary, it gives tractable and manageable formulas with minimum
mathematical prerequisites. Moreover, knowing only some associated matrices of the matrix, we can simply provide the
minimal polynomial of this matrix.

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Bibliographies de l'auteur

Said Zriaa, Université Chouaïb Doukkali

Department of Mathematics

Mohammed Mouçouf, University Chouaïb Doukkali

Department of Mathematics

Références

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M. Moucouf. P-canonical forms and Drazin inverses. arXiv:2007.10199v4 [math.RA](2021).

M. Moucouf, S. Zriaa. A new approach for computing the inverse of confluent Vandermonde matrices via Taylor's expansion. Linear Multilinear Algebra (2021). DOI:10.1080/03081087.2021.1940807.

M. Moucouf, S. Zriaa. Explicit formulas for the matrix exponential. Accepted for publication in Boletim da Sociedade Paranaense de Matematica (2022).

A. Spitzbart. A generalization of Hermite's interpolation formula. Am Math Mon. 1960;67(1):42-46.

Publiée
2024-05-07
Rubrique
Research Articles