{"paper":{"title":"Generalized Shemesh criterion, common invariant subspaces and irreducible completely positive superoperators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.QA","authors_text":"Andrzej Jamio{\\l}kowski, Grzegorz Pastuszak","submitted_at":"2013-06-01T07:21:30Z","abstract_excerpt":"Assume that $A_{1},...,A_{s}$ are complex $n\\times n$ matrices. We give a computable criterion for existence of a common eigenvector of $A_{i}$ which generalize the result of D. Shemesh established for two matrices. We use this criterion to prove some necessary and sufficient condition for $A_{i}$ to have a common invariant subspace of dimension $d$, $2\\leq d<n$, if every $A_{i}$ has pairwise different eigenvalues. Finally, we observe that the set of all matrices having multiple eigevalues has Lebesgue measure 0 and thus the condition is sufficient in practical applications. Being motivated by"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0083","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"}