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Schur complements of diagonally dominant matrices. (English) Zbl 0423.15008


MSC:

15B57 Hermitian, skew-Hermitian, and related matrices
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References:

[1] Arthur Albert: Conditions for positive and nonnegative definiteness in terms of pseudo inverses. SIAM J. Appl. Math. 17 (1969), 434-440. · Zbl 0265.15002
[2] David Carlson: Matrix decompositions involving the Schur complement. SIAM J. AppL Math. 28(1975), 577-587. · Zbl 0296.15006
[3] Douglas Crabtree: Applications of \(M\)-matrices to nonnegative matrices. Duke Math. J., 33 (1966), 197-208. · Zbl 0142.27101
[4] Douglas Crabtree, Emilie V. Haynsworth: An identity for the Schur complement of a matrix. Proc. Amer. Math. Soc. 22 (1969), 364-366. · Zbl 0186.34003
[5] Miroslav Fiedler, Vlastimil Pták: On matrices with nonpositive off-diagonal elements and positive principal minors. Czech. Math. J. 12 (87) (1962), 382-400. · Zbl 0131.24806
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[8] Emilie V. Haynsworth: Determination of the inertia of a partitioned hermitian matrix. Lin. Alg. Appl. 1 (1967), 73-82. · Zbl 0155.06304
[9] M. S. Lynn: On the Schur product of \(H\)-matrices and nonnegative matrices, and related inequalities. Proc. Camb. Phil. Soc. 60 (1964), 425 - 431. · Zbl 0145.24902
[10] Marvin Marcus, Henryk Mine: A Survey of Matrix Theory and Matrix Inequalities. Allyn and Bacon, Boston, 1964.
[11] Olga Taussky: A recurring theorem on determinants. American Mathematical Monthly, 56 (1949), 672-676. · Zbl 0036.01301
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