{"paper":{"title":"Generic canonical forms for perplectic and symplectic normal matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.RA","authors_text":"Philip Saltenberger, Ralph John de la Cruz","submitted_at":"2020-06-27T08:30:31Z","abstract_excerpt":"Let $B$ be some invertible Hermitian or skew-Hermitian matrix. A matrix $A$ is called $B$-normal if $AA^\\star = A^\\star A$ holds for $A$ and its adjoint matrix $A^\\star := B^{-1}A^HB$. In addition, a matrix $Q$ is called $B$-unitary, if $Q^HBQ = B$. We develop sparse canonical forms for nondefective (i.e. diagonalizable) $J_{2n}$-normal matrices and $R_n$-normal matrices under $J_{2n}$-unitary ($R_n$-unitary, respectively) similarity transformations where $$J_{2n} = \\begin{bmatrix} & I_n \\\\ - I_n & \\end{bmatrix} \\in M_{2n}(\\mathbb{C})$$ and $R_n$ is the $n \\times n$ sip matrix with ones on its"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.16790","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.16790/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}