Geodesic
Solvability of matrix equations in rings of quasi-diagonal matrices and similarity of matrix polynomials
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 8, pp. 1353-1362 Cet article a éte moissonné depuis la source Math-Net.Ru

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A certain standard form is found for a complex matrix with respect to equivalent transformations by quasi-diagonal matrices. The solvability of certain matrix equations in the rings of quasi-diagonal matrices is examined using this standard form. 
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B. Z. Shavarovskii. Solvability of matrix equations in rings of quasi-diagonal matrices and similarity of matrix polynomials. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 8, pp. 1353-1362. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_8_a1/

[1] Ikramov Kh. D., Chislennye metody resheniya matrichnykh uravnenii, Nauka, M., 1984 | MR | Zbl

[2] Ikramov Kh. D., “Ob odnom kriterii kvazidiagonalizuemosti veschestvennykh matrits”, Zh. vychisl. matem. i matem. fiz., 40:1 (2000), 6–20 | MR | Zbl

[3] Drozd Yu. A., “O ruchnykh i dikikh matrichnykh zadachakh”, Matrichnye zadachi, IM AN USSR, Kiev, 1977, 104–114 | MR

[4] Shavarovskii B. Z., “Poluskalyarnaya ekvivalentnost polinomialnykh matrits s poparno razlichnymi kornyami ikh kharakteristicheskogo mnogochlena”, Matem. metody i fiz.-mekhan. polya, 19, Nauk. dumka, Kiev, 1984, 33–37 | MR

[5] Shavarovskii B. Z., “Reduktsiya matrits pri pomoschi ekvivalentnykh i podobnykh preobrazovanii”, Matem. zametki, 64:5 (1998), 769–782 | MR

[6] Kazimirskii P. S., Petrichkovich V. M., “Odno dostatochnoe uslovie razlozhimosti matrichnogo kvadratnogo trekhchlena na lineinye mnozhiteli”, II Vses. simpozium po teorii kolets, algebr i modulei, Shtiintsa, Kishinev, 1974, 29–30

[7] Krupnik I. N., “O razlozhenii matrichnogo puchka na lineinye mnozhiteli”, Matem. zametki, 49:2 (1991), 95–101 | MR | Zbl

[8] Krupnik I., “Decomposition of a monic matrix polynomial into a product of linear factors”, Linear Algebra and Appl., 167 (1992), 239–242 | DOI | MR

[9] Shavarovskii B. Z., “O razlozhimykh mnogochlennykh matritsakh”, Matem. zametki, 68:4 (2000), 593–607 | MR

[10] Kazimirskii P. S., Rozklad matrichnikh mnogochleniv na mnozhniki, Nauk. dumka, Kiïv, 1981

[11] Newman M., “On the Smith normal form”, J. Res. Bur. Standard. Sect. B, 75 (1971), 81–84 | MR | Zbl