{"ID":6620524,"CreatedAt":"2026-07-15T01:01:48.440468303Z","UpdatedAt":"2026-07-15T03:28:55.185153975Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.12431","arxiv_id":"2607.12431","title":"Local Maxima of the Entrywise $\\ell_4$ Norm on the Orthogonal Group","abstract":"We classify the local maximizers of the entrywise fourth-power objective \\[ Q\\longmapsto \\lVert Q\\rVert_4^4 =\\sum_{i,j=1}^r q_{ij}^4 \\] 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 $Q^{\\circ2}$: 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.","short_abstract":"We classify the local maximizers of the entrywise fourth-power objective \\[ Q\\longmapsto \\lVert Q\\rVert_4^4 =\\sum_{i,j=1}^r q_{ij}^4 \\] 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. M...","url_abs":"https://arxiv.org/abs/2607.12431","url_pdf":"https://arxiv.org/pdf/2607.12431v1","authors":"[\"Dian Jin\"]","published":"2026-07-14T07:01:35Z","proceeding":"eess.SP","tasks":"[\"eess.SP\"]","methods":"[]","has_code":false}