Geodesic
Hölder rigidity for matrices
Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 4, pp. 225-233
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It is proved that a $(C_{1},C_{2})$-Hölder valuation is $(2,\alpha)$-equivalent to classical valuation on the set of matrices over a skew field and on the set of cubic matrices over a field. These results provide an extension of the Garcia theorem. 
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M. H. Hosseini. Hölder rigidity for matrices. Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 4, pp. 225-233. http://geodesic.mathdoc.fr/item/FPM_2004_10_4_a13/

[1] Sokolov N. P., Prostranstvennye matritsy i ikh prilozheniya, Fizmatlit, M., 1960 | MR | Zbl

[2] Cohn P. M., “The construction of valuations on skew fields”, J. Indian Math. Soc., 54 (1989), 1–45 | MR | Zbl

[3] Cohn P. M., Skew Fields, Theory of General Division Rings, Cambridge University Press, Cambridge, 1995 | MR | Zbl

[4] Lecat M., “Coup d'oeil sur la theorie des determinants superieurs dans son état actuel, II”, Ann. Soc. Sci. Bruxelles, 45:1, 2 (1926), 1–98 ; 3, 4, 141–168; 46 (1926), 15–54; 47:1 (1927), 1–37, serie A, II | MR

[5] Mahdavi-Hezavehi M., “Matrix valuations and their associated skew fields”, Resultate d. Math., 5 (1982), 149–156 | MR | Zbl

[6] Munoz Garcia E., “Hoelder absolute values are equivalent to classical ones”, Proc. Amer. Math. Soc., 127:7 (1999), 1967–1971 | DOI | MR | Zbl

[7] Rice L. H., “Introduction to higher determinants”, J. Math. Phys., 9 (1930), 47–71