Geodesic
On some properties of mixed discriminants
Sbornik. Mathematics, Tome 56 (1987) no. 2, pp. 279-293 
A. A. Panov. On some properties of mixed discriminants. Sbornik. Mathematics, Tome 56 (1987) no. 2, pp. 279-293. http://geodesic.mathdoc.fr/item/SM_1987_56_2_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this article known results of A. D. Aleksandrov concerning mixed discriminants, connected with positive definite quadratic forms, are carried over to the case of positive semidefinite quadratic forms. In particular, the analogue of the Frobenius–Koenig theorem is proved for mixed discriminants, and the main result is the derivation of a necessary and sufficient condition for equality to hold in Aleksandrov's inequality. Bibliography: 8 titles.

[1] Aleksandrov A. D., “K teorii smeshannykh ob'emov vypuklykh tel. IV. Smeshannye diskriminanty i smeshannye ob'emy”, Matem. sb., 3(45) (1938), 227–251 | Zbl

[2] Egorychev G. P., “Dokazatelstvo gipotezy Van der Vardena dlya permanentov”, SMZh, 22:6 (1981), 65–71 | MR | Zbl

[3] Falikman D. I., “Dokazatelstvo gipotezy Van der Vardena o permanente dvazhdy stokhasticheskoi matritsy”, Matem. zametki, 29:6 (1981), 931–938 | MR | Zbl

[4] Mink Kh., Permanenty, Mir, M., 1982 | MR

[5] Burago D. M., Zalgaller V. A., Geometricheskie neravenstva, Nauka, L., 1980 | MR | Zbl

[6] Kostrikin A. I., Manin Yu. I., Lineinaya algebra i geometriya, MGU, M., 1980 | MR

[7] Panov A. A., “O signature i yadre bilineinoi formy, svyazannoi s permanentom”, UMN, 6 (1984), 201–202 | MR | Zbl

[8] Panov A. A., “O smeshannykh diskriminantakh, svyazannykh s polozhitelno-poluopredelennymi kvadratichnymi formami”, DAN SSSR, 282:2 (1985), 273–276 | MR | Zbl