Geodesic
Balance relation for the spectral characteristics of a multiparameter polynomial matrix
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXII, Tome 367 (2009), pp. 187-194 
V. B. Khazanov. Balance relation for the spectral characteristics of a multiparameter polynomial matrix. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXII, Tome 367 (2009), pp. 187-194. http://geodesic.mathdoc.fr/item/ZNSL_2009_367_a11/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The known balance relation interrelating the spectrum multiplicities and the sums of mini-indices of a one-parameter polynomial matrix with its degree and rank is generalized to the case of a multiparameter polynomial matrix. Bibl. – 6 titles.

[1] V. N. Kublanovskaya, V. B. Khazanov, Chislennye metody resheniya parametricheskikh zadach algebry.Chast 1. Odnoparametricheskie zadachi, Nauka, S.-Pb., 2004

[2] V. B. Khazanov, “O spektralnykh svoistvakh $\lambda$-matrits”, Zap. nauchn. semin. LOMI, 111, 1981, 180–194 | MR | Zbl

[3] V. B. Khazanov, “O spektralnykh svoistvakh mnogoparametricheskikh polinomialnykh matrits”, Zap. nauchn. semin. POMI, 229, 1995, 284–321 | MR | Zbl

[4] V. B. Khazanov, “O nekotorykh svoistvakh polinomialnykh bazisov podprostranstv nad polem ratsionalnykh funktsii mnogikh peremennykh”, Zap. nauchn. semin. POMI, 284, 2002, 177–191 | MR | Zbl

[5] V. B. Khazanov, “Rezultantnyi podkhod k vychisleniyu vektornykh kharakteristik mnogoparametricheskikh polinomialnykh matrits”, Zap. nauchn. semin. POMI, 323, 2005, 182–214 | MR | Zbl

[6] G. D. Forney, “Minimal bases of rational vector spaces with applications to multivariable linear systems”, SIAM J. Control, 13:3 (1975), 182–214 | DOI | MR