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The inertia of a Hermitian matrix having prescribed complementary principal submatrices. (English) Zbl 0456.15011


MSC:

15A42 Inequalities involving eigenvalues and eigenvectors
15A18 Eigenvalues, singular values, and eigenvectors
15A21 Canonical forms, reductions, classification
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[1] Cain, B. E., Inertia theory for operators on a Hilbert space, (Ph.D. Thesis (1968), Univ. of Wisconsin: Univ. of Wisconsin Madison, Wis.) · Zbl 0475.47015
[2] Carlson, D.; Schneider, H., Inertia theorems for matrices: the semidefinite case, J. Math. Anal. Appl., 6, 430-446 (1963) · Zbl 0192.13402
[3] Cottle, R. W., Manifestations of the Schur Complement, Linear Algebra and Appl., 8, 189-211 (1974) · Zbl 0284.15005
[4] Haynsworth, E. V., Determination of the inertia of a partitioned Hermitian matrix, Linear Algebra and Appl., 1, 73-81 (1968) · Zbl 0155.06304
[5] Haynsworth, E. V.; Ostrowski, A. M., On the inertia of some classes of partitioned matrices, Linear Algebra and Appl., 1, 299-316 (1968) · Zbl 0186.33704
[6] Marques de Sá, E., On the inertia of sums of Hermitian matrices, Linear Algebra and Appl., 37, 143-159 (1983), (previous paper) · Zbl 0457.15012
[7] Thompson, R. C.; Freede, L. J., On the eigenvalues of sums of Hermitian matrices, Linear Algebra and Appl., 4, 369-376 (1971) · Zbl 0228.15005
[8] Thompson, R. C.; Therianos, S., The eigenvalues of complementary principal submatrices of a positive definite matrix, Canad. J. Math., 24, 658-667 (1972) · Zbl 0256.15012
[9] Wimmer, H. K., On the Ostrowski-Schneider inertia theorem, J. Math. Anal. Appl., 41, 164-169 (1973) · Zbl 0251.15011
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