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60 CARLOS M. DA FONSECA
[7] J. Dancis, The possible inertias for a Hermitian matrix and its principal submatrices, Linear Algebra Appl. 85 (1987), 121 − 151.
[8] J. Dancis, Several consequences of an inertia theorem, Linear Algebra Appl. 136 (1990), 43 − 61.
[9] J. Dancis, Choosing the inertias for completions of certain partially specified matrices, SIAM J. Matrix Anal. Appl. 14 (1993), 813 − 829.
[10] J. Dancis, Ranks and inertias of Hermitian block Toeplitz matrices, Linear Algebra Appl. 353 (2002), 21 − 32.
[11] C.M. da Fonseca, The inertia of certain Hermitian block matrices, Linear Algebra Appl., 274 (1998), 193 − 210.
[12] C.M. da Fonseca, The inertia of Hermitian block matrices with zero main diagonal, Linear Algebra Appl. 311 (2000), 153 − 160.
[13] C.M. da Fonseca, The inertia of Hermitian tridiagonal block matrices, JIPAM. J. In- equal. Pure Appl. Math. 5 (2004), Article 56.
[14] C.M. da Fonseca, A conjecture about the inertia of Hermitian matrices, Math. Inequal. Appl. 7 (2004), 497 − 503.
[15] E.V. Haynsworth, Determination of the inertia of some partitioned Hermitian matrices, Linear Algebra Appl. 1 (1968), 73 − 81.
[16] E.V. Haynsworth and A.M. Ostrowski, On the inertia of some classes of partitioned matrices, Linear Algebra Appl. 1 (1968), 299 − 316.
[17] R. Loewy, On ranges of Lyapunov transformations. II, Linear Multilinear Algebra 2 (1974/75), 227 − 237.
[18] E. Marques de Sa´, On the inertia of sums of Hermitian matrices, Linear Algebra Appl. 37 (1981), 143 − 159.
[19] A. Ostrowski and Hans Schneider, Some theorems on the inertia of general matrices, J. Math. Anal. Appl 4 (1962), 72 − 84.
Departamento de Matema´tica Universidade de Coimbra 3001-454 Coimbra, Portugal E-mail address: cmf@mat.uc.pt