{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T05:04:29Z","timestamp":1750309469932,"version":"3.41.0"},"reference-count":8,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2024,9,1]],"date-time":"2024-09-01T00:00:00Z","timestamp":1725148800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2024,9]]},"abstract":"<jats:p>\n            In this extended abstract, we describe recent progress on finding conditions for eigenvalue configurations of two real symmetric matrices. To illustrate the problem, consider a simple example. Let\n            <jats:italic>F<\/jats:italic>\n            and\n            <jats:italic>G<\/jats:italic>\n            be 2 \u00d7 2 real symmetric matrices. Since the matrices are symmetric, their eigenvalues are all real. Thus we may consider the configuration (relative locations of) of the two eigenvalues of\n            <jats:italic>F<\/jats:italic>\n            and the two eigenvalues of\n            <jats:italic>G<\/jats:italic>\n            on the real line. The problem is, given a certain configuration of those eigenvalues, to find a simple condition on the entries of\n            <jats:italic>F<\/jats:italic>\n            and\n            <jats:italic>G<\/jats:italic>\n            so that the eigenvalues satisfy the given configuration. For a more precise statement of the problem, see Section 1.\n          <\/jats:p>","DOI":"10.1145\/3717582.3717587","type":"journal-article","created":{"date-parts":[[2025,2,11]],"date-time":"2025-02-11T20:41:51Z","timestamp":1739306511000},"page":"72-76","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Conditions for Eigenvalue Configurations of Two Real Symmetric Matrices"],"prefix":"10.1145","volume":"58","author":[{"given":"Hoon","family":"Hong","sequence":"first","affiliation":[{"name":"Department of Mathematics, North Carolina State University, USA"}]},{"given":"Daniel","family":"Profili","sequence":"additional","affiliation":[{"name":"Department of Mathematics, North Carolina State University, USA"}]},{"given":"J. Rafael","family":"Sendra","sequence":"additional","affiliation":[{"name":"Department of Quantitative Methods, CUNEF-University, Spain"}]}],"member":"320","published-online":{"date-parts":[[2025,2,11]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Texts and Monographs in Symbolic Computation","author":"Caviness Bob F.","year":"2004","unstructured":"Bob F. Caviness and Jeremy R. Johnson. Quantifier elimination and cylindrical algebraic decomposition. In Texts and Monographs in Symbolic Computation, 2004."},{"key":"e_1_2_1_2_1","volume-title":"Quantifier elimination for real closed fields by cylindrical algebraic decomposition. Lecture notes in computer science, 33:515--532","author":"Collins George E.","year":"1975","unstructured":"George E. Collins. Quantifier elimination for real closed fields by cylindrical algebraic decomposition. Lecture notes in computer science, 33:515--532, 1975."},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0747-7171(08)80152-6"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/36.5.399"},{"key":"e_1_2_1_5_1","volume-title":"Symmetric functions and Hall polynomials","author":"Macdonald Ian Grant","year":"1998","unstructured":"Ian Grant Macdonald. Symmetric functions and Hall polynomials. Oxford university press, 1998."},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(86)90029-2"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1525\/9780520348097"},{"key":"e_1_2_1_8_1","volume-title":"Geometry of the signed support of a multivariate polynomial and descartes' rule of signs. arXiv preprint arXiv:2310.05466","author":"Telek M\u00e1t\u00e9 L","year":"2023","unstructured":"M\u00e1t\u00e9 L Telek. Geometry of the signed support of a multivariate polynomial and descartes' rule of signs. arXiv preprint arXiv:2310.05466, 2023."}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3717582.3717587","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3717582.3717587","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T01:17:15Z","timestamp":1750295835000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3717582.3717587"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9]]},"references-count":8,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["10.1145\/3717582.3717587"],"URL":"https:\/\/doi.org\/10.1145\/3717582.3717587","relation":{},"ISSN":["1932-2232","1932-2240"],"issn-type":[{"type":"print","value":"1932-2232"},{"type":"electronic","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2024,9]]},"assertion":[{"value":"2025-02-11","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}