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


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[1] Gantmacher, F. R., (The Theory of Matrices, Vol. II (1959), Chelsea: Chelsea New York) · Zbl 0085.01001
[2] Sylvester, J. J., Math. Papers I, 378-381 (1904), Cambridge
[3] Bellman, R., Introduction to Matrix Analysis (1960), McGraw-Hill: McGraw-Hill New York · Zbl 0124.01001
[4] Lyapunov, A., (Annals of Mathematical Studies, Vol. 17 (1947), Princeton Univ. Press: Princeton Univ. Press Princeton, N.J)
[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 Univ. Press Cambridge · Zbl 0043.32504
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