2026/07/14 by Dian Jin
Engineering · Mathematics · #eess.SP #math.OC
arxiv created 2026/07/30 · arxiv updated 2026/07/31
We classify the local maximizers of the entrywise fourth-power objective Q\longmapsto ‖ Q‖44 =∑i,j=1r qij4 over the real orthogonal group \mathcal O(r). We prove that the signed permutation matrices are the only local maximizers, and hence the only global maximizers, in every dimension. More strongly, every other stationary point has an explicit rank-two tangent direction with strictly positive second variation. The proof is based on a maximum-entry pivot for the orthostochastic matrix Q∘2: the associated full Riemannian Hessian can be evaluated exactly and is positive at a largest nonunit squared entry. The argument is self-contained and handles zeros, repeated magnitudes, reducible support, and Hadamard-type stationary points.