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We develop a framework for answering geometric and analytic (both classical and nonsmooth) questions about such a function by answering the corresponding question for the (much simpler) function appearing in the decomposition. The aim is to understand and extend the foundations of eigenvalue optimization, matrix approximation, and semidefinite programming.<\/jats:p>","DOI":"10.1137\/s0895479895283173","type":"journal-article","created":{"date-parts":[[2005,2,27]],"date-time":"2005-02-27T07:15:07Z","timestamp":1109488507000},"page":"927-949","source":"Crossref","is-referenced-by-count":50,"title":["Group Invariance and Convex Matrix Analysis"],"prefix":"10.1137","volume":"17","author":[{"given":"A. 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