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Positive Powers of Positive Positive Definite Matrices

Published online by Cambridge University Press:  20 November 2018

Lon Rosen
Lon Rosen*
Affiliation:
Mathematics Department University of British Columbia Vancouver, B.C. V6T 1Z2, e-mail: rosen@math.ubc.ca
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Abstract

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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 Cp ≥ 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.

Keywords

15A4847A6360J15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 1 , 01 February 1996 , pp. 196 - 209
Copyright
Copyright © Canadian Mathematical Society 1997

References

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