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Cyclic products and an inequality for determinants. (English) Zbl 0281.15014


MSC:

15A42 Inequalities involving eigenvalues and eigenvectors
15A15 Determinants, permanents, traces, other special matrix functions
15B48 Positive matrices and their generalizations; cones of matrices
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References:

[1] M. Fiedler V. Pták: On Matrices with Non-positive Off-diagonal Elements and Positive Principal Minors. Czech. Math. J. 87 (1962), 382-400. · Zbl 0131.24806
[2] K. Goldberg: A Matrix with Real Characteristic Roots. J. Res. NBS 56 (1956). · Zbl 0074.25402
[3] K. Goldberg: Random Notes on Matrices. J. Res. NBS 60 (1958), 321–325. · Zbl 0089.00901
[4] Д. М. Котелянский: Осонки для определителей матриц с преобладающей главной диагоналю. Изь. АН СССР д3єг. мат. 20 (1956), 137-144. · Zbl 0995.90522
[5] A. Ostrowski: Determinanten mit überwiegender Hauptdiagonale und die absolute Konvergenz von linearen Iterationsprozessen. Comm. Math. Helv. 30 (1956), 175-210. · Zbl 0072.13803
[6] V. Pták: On a Combinatorial Theorem and Its Application to Nonnegative Matrices. Czech. Math. J. 83 (1958), 487-495. · Zbl 0082.24402
[7] V. Pták J. Sedláček: On the Index of Imprimitivity of Nonnegative Matrices. Czech. Math. J. 83 (1958), 495-501. · Zbl 0082.24403
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