TITLE

# Semiconvexity of invariant functions of rectangular matrices

AUTHOR(S)
M. Silhavý
PUB. DATE
May 2003
SOURCE
Calculus of Variations & Partial Differential Equations;May2003, Vol. 17 Issue 1, p75
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
Abstract. The paper deals with the semiconvexity properties (i.e., the rank 1 convexity, quasiconvexity, polyconvexity, and convexity) of rotationally invariant functions f of $m/FORMULA> matrices. For$m\neq n$the invariance with respect to the proper orthogonal group and the invariance with respect to the full orthogonal group coincide. With each invariant f one can associate a fully invariant function$f_\flat$of a square matrix of type$p\times p$where$p = \min \{m,n\}.$It is shown that f has the semi convexity of a given type if and only if$f_\flat$has the semiconvexity of that type. Consequently the semiconvex hulls of f can be determined by evaluating the corresponding hulls of$f_\flat$and then extending them to$m/FORMULA> matrices by rotational invariance.
ACCESSION #
12008081

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