Abstract
In this chapter we investigate three subjects concerning the convexity of functions defined on a space of matrices (or just on a convex subset of it). The first one is devoted to the convex spectral functions, that is, to the convex functions \(F:{\text {Sym}}(n,\mathbb {R})\rightarrow \mathbb {R}\) whose values F(A) depend only on the spectrum of A. The main result concerns their description as superpositions \(f\circ \Lambda \) between convex functions \(f:\mathbb {R}^{n}\rightarrow \mathbb {R}\) invariant under permutations, and the eigenvalues map \(\Lambda \).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
