most recent 30 from http://mathoverflow.net 2013-05-23T00:40:17Z http://mathoverflow.net/feeds/question/72190 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/72190/joint-convexity-of-spectral-functions-of-several-matrices Krishna 2011-08-05T16:26:51Z 2011-08-05T16:26:51Z

<p>${A_1 \ldots A_K }$ is a set of matrices in $\mathbb{R}^{m \times n}$. Let $f (A_1,\ldots,A_K)$ be a function of the singular values of all matrices. For e.g., $f$ is just summation of singular values of all matrices. But potentially I would like to find the class of such functions which are jointly convex in $A_1, \ldots, A_K$. Can necessary and sufficient conditions be established for a function to belong to such a class?</p>