Geodesic
On the Similarity of Matrices of Even Order
Matematičeskie zametki, Tome 81 (2007) no. 3, pp. 448-463.

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We study invariants of simultaneous similarity of a pair of matrices of even order $2k$ over the field of complex numbers for the case in which all elementary divisors of the corresponding characteristic polynomial matrix are identical and their number is $k$.
Keywords: similarity of matrices, characteristic polynomial matrix, semiscalarly equivalent transformation
Mots-clés : Jordan matrix. 
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B. Z. Shavarovskii. On the Similarity of Matrices of Even Order. Matematičeskie zametki, Tome 81 (2007) no. 3, pp. 448-463. http://geodesic.mathdoc.fr/item/MZM_2007_81_3_a12/

[1] B. Z. Shavarovskii, “Polnaya sistema invariantov pary matrits chetnogo poryadka so spetsialnoi formoi Smita ee kharakteristicheskoi matritsy otnositelno podobiya”, Matem. zametki, 73:6 (2003), 923–941 | MR | Zbl

[2] I. M. Gelfand, V. A. Ponomarev, “Nerazlozhimye predstavleniya gruppy Lorentsa”, UMN, 23:2 (1968), 3–60 | MR | Zbl

[3] L. A. Nazarova, A. V. Roiter, V. V. Sergeichuk, V. M. Bondarenko, “Primenenie modulei nad diadoi dlya klassifikatsii konechnykh $p$-grupp, obladayuschikh abelevoi podgruppoi indeksa $p$, i $n$ par vzaimno annuliruyuschikh operatorov”, Zapiski. nauch. sem. LOMI, 28, 1972, 69–92 | MR | Zbl

[4] V. M. Bondarenko, “Predstavleniya diedralnykh grupp nad polem kharakteristiki 2”, Matem. sb., 96 (138):1 (1975), 63–74 | MR | Zbl

[5] S. Friedland, “Simultaneous similarity of matrices”, Adv. Math., 50:3 (1983), 189–265 | DOI | MR | Zbl

[6] R. M. Bulatovich, “Odnovremennoe privedenie simmetricheskoi i kososimmetricheskoi matrits k kanonicheskomu vidu”, Mat. Tsrne Gore., 8 (1997), 33–36 | MR | Zbl

[7] Kh. D. Ikramov, “Ob odnovremennoi privodimosti k blochno-treugolnomu vidu par kosykh proektorov”, ZhVM i MF, 38:2 (1998), 181–182 | MR | Zbl

[8] Kh. D. Ikramov, “Ob odnom kriterii kvazidiagonalizuemosti veschestvennykh matrits”, ZhVM i MF, 40:1 (2000), 6–20 | MR | Zbl

[9] G. R. Belitskii, “Normal form in matrix spaces”, Integral Equations Operator Theory, 38:3 (2000), 251–283 | DOI | MR | Zbl

[10] V. V. Sergeichuk, “Canonical matrices for linear matrix problem”, Linear Algebra Appl., 317:1–3 (2000), 53–102 | DOI | MR | Zbl

[11] V. V. Sergeichuk, “Klassifikatsionnye zadachi dlya sistem form i lineinykh otobrazhenii”, Izv. AN SSSR. Ser. matem., 51:6 (1987), 1170–1190 | MR | Zbl

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

[13] B. Z. Shavarovskii, “Kanonicheskaya forma mnogochlennoi matritsy s odnim elementarnym delitelem otnositelno poluskalyarno ekvivalentnykh preobrazovanii”, Dokl. AN USSR. Ser. A. Fiz.-mat. i tekhn. nauki, 1988, no. 10, 32–35 | MR | Zbl

[14] P. S. Kazimirskii, Rozklad matrichnikh mnogochleniv na mnozhniki, Naukova dumka, Kiïv, 1981

[15] F. R. Gantmakher, Teoriya matrits, Nauka, M., 1988 | MR | Zbl