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Inertia theorems for matrices: the semidefinite case. (English) Zbl 0192.13402

##### Keywords:
linear algebra, forms
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##### References:
 [1] Gantmacher, F.R; Gantmacher, F.R, () [2] Sylvester, J.J; Sylvester, J.J; Sylvester, J.J, A demonstration of the theorem that every homogeneous quadratic polynomial is reducible by real orthogonal substitutions to the form of a sum of positive and negative squares, Phil. mag., Phil. mag., Math. papers I, 142, 378-381, (1904), Cambridge [3] Bellman, R, Introduction to matrix analysis, (1960), McGraw-Hill New York · Zbl 0124.01001 [4] Lyapunov, A; Lyapunov, A, Problème Général de la stabilité du mouvement, (), (1892), 1893 [5] Taussky, O, A remark on a theorem by Lyapunov, J. math. anal. appl., 2, 105-107, (1961) · Zbl 0158.28203 [6] Taussky, O, A generalization of a theorem by Lyapunov, J. soc. ind. appl. math., 9, 640-643, (1961) · Zbl 0108.01202 [7] Ostrowski, A; Schneider, H, Some theorems on the inertia of general matrices, J. math. anal. appl., 4, 72-84, (1962) · Zbl 0112.01401 [8] Givens, W, Elementary divisors and some properties of the Lyapunov mapping $$X → AX + XA\^{}\{∗\}$$, Argonne natl. lab. report ANL-6546, (1961) [9] Cauchy, A, Sur l’équation à l’aide de laquelle on détermine LES inégalités séculaires des mouvements des planètes, Ouevres complètes, iie série, 9, 174-195, (1829) [10] Beckenbach, E.F; Bellman, R, Inequalities, Ergeb. math. u. grenzg. N.F., 30, (1961) · Zbl 0513.26003 [11] Hamburger, H.L; Grimshaw, M.E, Linear transformations in n-dimensional vector space, (1951), Cambridge Univ. Press Cambridge · Zbl 0043.32504
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