On matrices with non-positive off-diagonal elements and positive principal minors. (English) Zbl 0131.24806


15A15 Determinants, permanents, traces, other special matrix functions
15A42 Inequalities involving eigenvalues and eigenvectors
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[1] K. Fan: Topological proofs for certain theorems on matrices with non-negative elements. Monatsh. Math. 62 (1958), 219-237. · Zbl 0081.25104 · doi:10.1007/BF01303967
[2] K. Fan: Note on M-matrices. Quart. J. Math. 11 (1960), 43-49. · Zbl 0104.01203 · doi:10.1093/qmath/11.1.43
[3] K. Fan A. J. Hoffman: Lower bounds for the rank and location of the eigenvalues of a matrix. Contributions to the solution of systems of linear equations and the determination of eigenvalues. NBS Appl. Math. Ser. 39, 117-130.
[4] K. Fan A. S. Householder: A note concerning positive matrices and M-matrices. Monatshefte Math. 63 (1959), 265-270. · Zbl 0086.01504 · doi:10.1007/BF01295199
[5] Д. М. Комелянскш: Оценки для определителей матриц с преобладающей главной диагональю. NAH, cep. matem., 20 (1956), 137-144. · Zbl 0995.90520 · doi:10.1287/mnsc.3.1.33
[6] A. Ostrowski: Determinanten mit überwiegender Hauptdiagonale und die absolute Konvergenz von linearen Iterationsprozessen. Commentarii Math. Helv. 3^\circ (1956), 175 - 210. · Zbl 0072.13803 · doi:10.1007/BF02564340
[7] R. S. Varga: On a lemma of Stieltjes on matrices. Westinghouse Technical Report WAPD-T-566.
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