Geodesic
On the Simultaneous Triangulability of Matrices
Matematičeskie zametki, Tome 68 (2000) no. 5, pp. 648-652.

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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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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/

[1] McCoy N. H., “On the characteristic roots of matrix polynomials”, Bull. Amer. Math. Soc., 42 (1936), 592–600 | DOI | Zbl

[2] Khorn R., Dzhonson Ch., Matrichnyi analiz, Mir, M., 1989

[3] Ikramov Kh. D., Saveleva N. V., Chugunov V. N., “O ratsionalnykh kriteriyakh suschestvovaniya obschikh sobstvennykh vektorov ili invariantnykh podprostranstv”, Programmirovanie, 1997, no. 3, 43–57 | MR | Zbl

[4] Drazin M. P., Dungey J. W., Gruenberg K. W., “Some theorems on commutative matrices”, J. London Math. Soc., 26 (1951), 221–228 | DOI | MR | Zbl

[5] Prasolov V. V., Zadachi i teoremy lineinoi algebry, Nauka, M., 1996 | Zbl

[6] Bakhturin Yu. A., Osnovnye struktury sovremennoi algebry, Nauka, M., 1990 | Zbl

[7] Kaplanskii I., Algebry Li i lokalno kompaktnye gruppy, Mir, M., 1974

[8] Ikramov Kh. D., Zadachnik po lineinoi algebre, Nauka, M., 1975

[9] McCoy N. H., “On quasi-commutative matrices”, Trans. Amer. Math. Soc., 36 (1934), 327–340 | DOI | MR | Zbl

[10] Drazin M. P., “Some generalizations of matrix commutativity”, Proc. London Math. Soc., 1 (1951), 222–231 | DOI | MR | Zbl

[11] Postnikov M. M., Gruppy i algebry Li, Nauka, M., 1982

[12] Pirs R., Assotsiativnye algebry, Mir, M., 1986

[13] Chebotarev N. G., Vvedenie v teoriyu algebr, Gostekhizdat, M., 1949