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The same correspondence holds for rational block Krylov subspaces and matrix-valued rational functions, and in the extended Krylov setting this leads naturally to Laurent matrix polynomials.\n  When the matrix $A$ is normal, we prove that t","authors_text":"Michele Rinelli, Raf Vandebril","cross_cats":["cs.NA"],"headline":"Polynomial block Krylov subspaces are isometrically isomorphic to spaces of matrix polynomials of bounded degree under a no-deflation assumption.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-16T12:11:31Z","title":"Block Krylov subspaces and orthogonal matrix polynomials: a structural correspondence with applications to unitary matrices"},"references":{"count":27,"internal_anchors":0,"resolved_work":27,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"A. C. Antoulas.Approximation of large-scale dynamical systems, volume 6 ofAdvances in Design and Control. 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Theory, 4:1–85, 2008","work_id":"a3cec6d9-b18e-4d28-a05f-2f522a3294bc","year":2008},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"V. Druskin and L. Knizhnerman. Extended Krylov subspaces: approximation of the matrix square root and related functions.SIAM J. Matrix Anal. Appl., 19(3):755–771, 1998","work_id":"c97b3a08-33e1-4dcd-ae51-f5473e36a3f2","year":1998}],"snapshot_sha256":"a6665d1676e244968638fcf0738211fd6bd296b52277a85be3ddf67803221262"},"source":{"id":"2605.16954","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T19:29:46.713301Z","id":"944884ae-f01f-498c-ac46-834ca70ab65d","model_set":{"reader":"grok-4.3"},"one_line_summary":"Block Krylov subspaces correspond isometrically to matrix polynomial spaces, allowing transfer of Szegő recurrences and CMV frameworks to orthogonalize polynomial and extended block Krylov bases for unitary matrices.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Polynomial block Krylov subspaces are isometrically isomorphic to spaces of matrix polynomials of bounded degree under a no-deflation assumption.","strongest_claim":"Under a no-deflation assumption, polynomial block Krylov subspaces are isometrically isomorphic to spaces of matrix polynomials of bounded degree, providing a unified framework for the analysis and construction of orthonormal bases and recurrence relations; for unitary matrices this transfers the Szegő recurrence and CMV framework to yield efficient orthogonalization procedures.","weakest_assumption":"The no-deflation assumption on the block Krylov process, which is invoked to guarantee that the generated subspace has full dimension and that the isometric isomorphism to the matrix-polynomial space holds without breakdown (abstract, paragraph on polynomial block Krylov subspaces)."}},"verdict_id":"944884ae-f01f-498c-ac46-834ca70ab65d"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7131010cb3ca366fc9a722e3260fbb40c24e04fcdef5404f058376eada4792e1","target":"record","created_at":"2026-05-20T00:03:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bc4e5d1d62f1fb967a202bc51b31bf557cad54b0efc3f9d10a35f98e99a54feb","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-16T12:11:31Z","title_canon_sha256":"343438720a38e7a86951387ca3193e4bc8b23d7b956832338f09cd0d3d3a8ce9"},"schema_version":"1.0","source":{"id":"2605.16954","kind":"arxiv","version":1}},"canonical_sha256":"8e1506fdea0fd05744be05f1150d705fa4dfc321ab050c39c0730ef45187bd3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e1506fdea0fd05744be05f1150d705fa4dfc321ab050c39c0730ef45187bd3b","first_computed_at":"2026-05-20T00:03:32.737305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:03:32.737305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7+jc8zai41kQfBUh3Z5MGPbrciXz8If2qbDe59zXmNvk144wD/zMvh+8QmtRbJqmCobSG1vd3Iq/vaMHnWWCDg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:03:32.737902Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.16954","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7131010cb3ca366fc9a722e3260fbb40c24e04fcdef5404f058376eada4792e1","sha256:db62cb0a781e684ddb2b89951b2f312d3f04b27e2ae813193a690d0c98387be7"],"state_sha256":"dbce534cf7b8eeaace87ff74da354eda0fc453608327b056aaacb9f225b51529"}