Geodesic
Bounds for Characteristic Values of Positive Definite Matrices
Canadian mathematical bulletin, Tome 15 (1972) no. 1, pp. 51-56

Voir la notice de l'article provenant de la source Cambridge University Press

We consider the problem of determining the best possible bounds on the eigenvalues of an nth order positive definite matrix B, when the determinant (D) and trace (T) are given. A large variety of bounds on the eigenvalues are known when different information concerning B is available (see, for example, [1], [2]). Since D and T simply provide the geometric mean and arithmetic mean of the positive, real eigenvalues of B, the solution to the problem involves certain inequalities satisfied by these means (see [3] for such inequalities in a more general setting). A related problem in which the largest and smallest eigenvalue are known, and inequalities involving D and T are obtained, is described in [4]. 
Binding, P. A.; Hoskins, W. D.; Ponzo, P. J. Bounds for Characteristic Values of Positive Definite Matrices. Canadian mathematical bulletin, Tome 15 (1972) no. 1, pp. 51-56. doi: 10.4153/CMB-1972-011-6
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[1] 1. Bodewig, , Matrix calculus, North Holland, Amsterdam (1965), 69-70. Google Scholar

[2] 2. Zhong-Ci, Shi and Bo-Ying, Wang, Bounds for the determinant, characteristic roots and condition number of certain types of matrices, Chinese Math. 7 (1965), 21-40. Google Scholar

[3] 3. Cargo, and Shisha, , Bounds on ratios of means, J. Res. Nat. Bur. Standards Vol. 66B (1962), 169-170. Google Scholar

[4] 4. Mond, and Shisha, , Inequalities, Vol. II, Academic Press, New York (1970), 241-249. Google Scholar

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