Geodesic
On the Simultaneous Triangulability of Matrices
Matematičeskie zametki, Tome 68 (2000) no. 5, pp. 648-652 
Yu. A. Alpin; N. A. Koreshkov. On the Simultaneous Triangulability of Matrices. Matematičeskie zametki, Tome 68 (2000) no. 5, pp. 648-652. http://geodesic.mathdoc.fr/item/MZM_2000_68_5_a1/
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     title = {On the {Simultaneous} {Triangulability} of {Matrices}},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2000_68_5_a1/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Two necessary and sufficient criteria for the simultaneous triangulability of two complex matrices are established. Both of them admit a finite verification procedure. To prove the first criterion, classical theorems from Lie algebra theory are used, and known sufficient conditions of triangulability are also given a natural interpretation in terms of this theory. The other criterion is discussed in the framework of the associative algebras. Here the decisive fact is the Wedderburn theorem on the nilpotence of a finite-dimensional nilalgebra.

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