Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4599340 | Linear Algebra and its Applications | 2015 | 16 Pages |
Abstract
Consider the matrix power function Xp defined over the cone of positive definite matrices S++n. It is known that Xp is convex over S++n if pâ[â1,0]âª[1,2] and Xp is concave over S++n if pâ[0,1]. We show that the hypograph of Xp admits a free semidefinite representation if pâ[0,1] is rational, and the epigraph of Xp admits a free semidefinite representation if pâ[â1,0]âª[1,2] is rational.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
J. William Helton, Jiawang Nie, Jeremy S. Semko,