{"paper":{"title":"Generalization of Roth's solvability criteria to systems of matrix equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Andrii Dmytryshyn, Tetiana Klymchuk, Vladimir V. Sergeichuk, Vyacheslav Futorny","submitted_at":"2017-04-15T18:02:20Z","abstract_excerpt":"W.E. Roth (1952) proved that the matrix equation $AX-XB=C$ has a solution if and only if the matrices $\\left[\\begin{matrix}A&C\\\\0&B\\end{matrix}\\right]$ and $\\left[\\begin{matrix}A&0\\\\0&B\\end{matrix}\\right]$ are similar. A. Dmytryshyn and B. K{\\aa}gstr\\\"om (2015) extended Roth's criterion to systems of matrix equations $A_iX_{i'}M_i-N_iX_{i''}^{\\sigma_i} B_i=C_i$ $(i=1,\\dots,s)$ with unknown matrices $X_1,\\dots,X_t$, in which every $X^{\\sigma}$ is $X$, $X^T$, or $X^*$. We extend their criterion to systems of complex matrix equations that include the complex conjugation of unknown matrices. We al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04670","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}