Geodesic
On the multiplicities of eigenvalues of a pair of quadratic forms
Matematičeskoe obrazovanie, no. 3 (2024), pp. 26-30 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a pair of real quadratic forms, one of which is positive definite. It is proven that it is possible without calculating the eigenvalues of this pair of forms, to find out if any of them are multiples. One can also express the sum of the squares of the multiplicities of these numbers through the rank of some auxiliary matrix. 
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N. V. Ilyushechkin. On the multiplicities of eigenvalues of a pair of quadratic forms. Matematičeskoe obrazovanie, no. 3 (2024), pp. 26-30. http://geodesic.mathdoc.fr/item/MO_2024_3_a3/

[1] N. V. Efimov, E. R. Rozendorn, Lineinaya algebra i mnogomernaya geometriya, FIZMATLIT, M., 2004

[2] F. R. Gantmakher, Teoriya matrits, Nauka, M., 1988

[3] A. S. Mischenko, A. T. Fomenko, Kurs differentsialnoi geometrii i topologii, Faktorial Press, M., 2000

[4] A. I. Kostrikin, Vvedenie v algebru, v. 1, Osnovy algebry, FIZMATLIT, M., 2004

[5] B. Sturmfels, Solving Systems of polinomial equations, CMBS Regional Conferense Series in Mathematics, 97, American Mathematical Society, Providence, 2002

[6] C. W. Borchardt, “Neue Eigenschaft der Gleichung, mitderen Hülfe man die seculären Störungen der Planeten bestimmt”, Journal für die reine und angewandte Mathematik, 1846, no. 30, 38–45

[7] Yu. P. Kremneva, “Diskriminant kharakteristicheskogo uravneniya simmetricheskoi matritsy”, Izvestiya vuzov. Matem., 5:1 (1961), 90–97