Geodesic
Positive Powers of Positive Positive Definite Matrices
Canadian journal of mathematics, Tome 48 (1996) no. 1, pp. 196-209

Voir la notice de l'article provenant de la source Cambridge University Press

Let C be an n x n positive definite matrix. If C ≥ 0 in the sense that Cij ≥ 0 and if p > n — 2, then C p ≥ 0. This implies the following "positive minorant property" for the norms ‖A‖p = [tr(A*A)p/2]1/P . Let 2 < p ≠ 4, 6, ... . Then 0 ≤ A ≤ B => ‖A‖p ≥ ‖B‖P if and only if n < p/2 + 1.
DOI : 10.4153/CJM-1996-009-9
Mots-clés : 15A48, 47A63, 60J15 
Rosen, Lon. Positive Powers of Positive Positive Definite Matrices. Canadian journal of mathematics, Tome 48 (1996) no. 1, pp. 196-209. doi: 10.4153/CJM-1996-009-9
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