Geodesic
Factorability of polynomial matrices depending on the powers of their elementary divisors
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 7, pp. 1171-1184 Cet article a éte moissonné depuis la source Math-Net.Ru

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B. Z. Shavarovskii. Factorability of polynomial matrices depending on the powers of their elementary divisors. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 7, pp. 1171-1184. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_7_a0/

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

[2] Shavarovskii B.Z., “O klassakh razlozhimykh i nerazlozhimykh mnogochlennykh matrits i vzaimnom ikh raspolozhenii”, Dokl. RAN, 413:6 (2007), 738–742 | MR | Zbl

[3] Shavarovskii B.Z., “Multiplikativnaya struktura mnogochlennoi matritsy v zavisimosti ot ee elementarnykh delitelei”, Dokl. RAN, 417:2 (2007), 175–179 | MR | Zbl

[4] Shavarovskii B.Z., “Rozkladnist na liniini mnozhniki matrichnikh mnogochleniv z komutuyuchimi koefitsiєntami”, Ukraïnsk. matem. zh., 62:8 (2010), 1114–1123 | MR

[5] Petrichkovich V.M., “Pro kratnosti kharakteristichnikh koreniv, stepeni elementarnikh dilnikiv i faktorizatsiyu mnogochlennikh matrits”, Matem. metodi ta fiz.-mekh. polya, 48:2 (2005), 7–17 | MR

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

[7] Gohberg I., Lansaster P., Rodman L., Matrix Polynomials, Academic Press, New York, 1982 | MR | Zbl

[8] Kazimirskii P.S., Petrichkovich V.M., “Razlozhimost polinomialnykh matrits na lineinye mnozhiteli”, Matem. metody i fiz.-mekhan. polya, 8 (1978), 3–9

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

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

[11] Gelfand S.I., “O chisle reshenii kvadratnogo uravneniya”, Globus. Obschematematicheskii seminar, 1, MTsNMO, M., 2004, 124–133

[12] Kozlov V.V., “Ogranicheniya kvadratichnykh form na lagranzhevy ploskosti, kvadratnye matrichnye uravneniya i giroskopicheskaya stabilizatsiya”, Funkts. analiz i ego prilozh., 39:4 (2005), 32–47 | MR | Zbl

[13] Kozlov V.V., “Lineinye sistemy s kvadratichnym integralom i simplekticheskaya geometriya prostranstv Artina”, Prikl. matem. i mekhan., 68:3 (2004), 371–383 | MR | Zbl

[14] Petrichkovich V.M., “O chisle reshenii matrichnogo uravneniya”, Matem. metody i fiz.-mekhan. polya, 12 (1980), 56–58 | MR | Zbl

[15] Kirillov A.A., “O chisle reshenii uravneniya $X^2=0$ v treugolnykh matritsakh nad konechnym polem”, Funkts. analiz i ego prilozh., 29:1 (1995), 82–87 | MR | Zbl

[16] Ikramov Kh.D., Chislennoe reshenie matrichnykh uravnenii, Nauka, M., 1984 | MR | Zbl

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

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

[19] Sakhnovich L.A., “O faktorizatsii peredatochnykh operator-funktsii”, Dokl. AN SSSR, 226:4 (1976), 781–784 | MR | Zbl

[20] Markus A.S., Mereutsa I.V., “O nekotorykh svoistvakh prostykh $\lambda$-matrits”, Matem. issled., 10:3 (1975), 207–213 | MR | Zbl

[21] Kazimirskii P.S., “Vydelenie iz matrichnogo mnogochlena regulyarnogo lineinogo mnozhitelya prostoi struktury”, Teoreticheskie i prikladnye voprosy algebry i differentsialnykh uravnenii, I-t matem. AN USSR, Kiev, 1976, 29–40 | MR

[22] Shavarovskii B.Z., Preobrazovaniya podobiya matrichnykh mnogochlenov i ikh razlozhimost na mnozhiteli, Diss. $\dots$ kand. fiz.-mat. nauk, IPPMM, Lvov, 1985