Geodesic
Schur complements of diagonally dominant matrices
Czechoslovak Mathematical Journal, Tome 29 (1979) no. 2, pp. 246-251
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DOI : 10.21136/CMJ.1979.101601
Classification : 15A15 
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Carlson, David; Markham, Thomas L. Schur complements of diagonally dominant matrices. Czechoslovak Mathematical Journal, Tome 29 (1979) no. 2, pp. 246-251. doi: 10.21136/CMJ.1979.101601

[1] Arthur Albert: Conditions for positive and nonnegative definiteness in terms of pseudo inverses. SIAM J. Appl. Math. 17 (1969), 434-440. | DOI | MR

[2] David Carlson: Matrix decompositions involving the Schur complement. SIAM J. AppL Math. 28(1975), 577-587. | DOI | MR

[3] Douglas Crabtree: Applications of $M$-matrices to nonnegative matrices. Duke Math. J., 33 (1966), 197-208. | DOI | MR

[4] Douglas Crabtree, Emilie V. Haynsworth: An identity for the Schur complement of a matrix. Proc. Amer. Math. Soc. 22 (1969), 364-366. | DOI | MR

[5] Miroslav Fiedler, Vlastimil Pták: On matrices with nonpositive off-diagonal elements and positive principal minors. Czech. Math. J. 12 (87) (1962), 382-400. | MR

[6] Miroslav Fiedler, Vlastimil Pták: Diagonally dominant matrices. Czech. Math. J. 17 (92) (1967), 420-433. | MR

[7] F. R. Gantmacher: The theory of matrices. Vol. I. Chelsea, New York, 1959.

[8] Emilie V. Haynsworth: Determination of the inertia of a partitioned hermitian matrix. Lin. Alg. Appl. 1 (1967), 73-82. | DOI | MR

[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. | DOI | MR

[10] Marvin Marcus, Henryk Mine: A Survey of Matrix Theory and Matrix Inequalities. Allyn and Bacon, Boston, 1964. | MR

[11] Olga Taussky: A recurring theorem on determinants. American Mathematical Monthly, 56 (1949), 672-676. | DOI | MR

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