The ambient space if $ {\bf M}_n({\mathbb R})$ . Let us begin with facts. 1- The cone of positive semi-definite symmetric matrices is convex. 2- It is a little subtler that the cone $ K^+$ of matrices with non-negative determinant is rank-one convex; this is because $ \det(M+xy^T)=\det M+x^T\hat My$ , where $ \hat M$Read more
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