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 [6] Miroslav Fiedler, Vlastimil Pták: Diagonally dominant matrices. Czech. Math. J. 17 (92) (1967), 420-433. · Zbl 0178.03402 [7] F. R. Gantmacher: The theory of matrices. Vol. I. Chelsea, New York, 1959. · Zbl 0085.01001 [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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