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Wielandt’s proof of the exponent inequality for primitive nonnegative matrices. (English) Zbl 1006.15023

This note contains a facsimile, a transcription, and an English translation of the proof of the exponent inequality found in Wielandts mathematical diaries. Finally a commentary on the proof is presented.

MSC:

15A45 Miscellaneous inequalities involving matrices
15-03 History of linear algebra
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References:

[1] R.A. Brualdi, H.J. Ryser, Combinatorial Matrix Theory, Cambridge, 1991; R.A. Brualdi, H.J. Ryser, Combinatorial Matrix Theory, Cambridge, 1991 · Zbl 0746.05002
[2] F.G. Frobenius, Über Matrizen aus nicht negativen Elementen, Sitzungsber. K. Preuss. Akad. Wiss. Berlin (1912) 456-477; Ges. Abh. 3 (1968) 546-567; F.G. Frobenius, Über Matrizen aus nicht negativen Elementen, Sitzungsber. K. Preuss. Akad. Wiss. Berlin (1912) 456-477; Ges. Abh. 3 (1968) 546-567 · JFM 43.0204.09
[3] H. Wielandt, Unzerlegbare, nicht negative Matrizen, Math. Z. 52 (1950) 642-648 and Mathematische Werke/Mathematical Works, vol. 2, 100-106 de Gruyter, Berlin, 1996; H. Wielandt, Unzerlegbare, nicht negative Matrizen, Math. Z. 52 (1950) 642-648 and Mathematische Werke/Mathematical Works, vol. 2, 100-106 de Gruyter, Berlin, 1996
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