{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T02:04:41Z","timestamp":1760061881079},"reference-count":58,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2016,12,24]],"date-time":"2016-12-24T00:00:00Z","timestamp":1482537600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,3,16]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The present article is a survey on linear multivariable systems equivalences. We attempt a review of the most significant forms of system equivalence having as a starting point matrix transformations preserving certain aspects of their spectral structure. From a system theoretic point of view, the need for a variety of forms of polynomial matrix equivalences, arises from the fact that different types of spectral invariants give rise to different types of dynamics of the underlying linear system. A historical perspective of the key results and their contributors is also given.<\/jats:p>","DOI":"10.1093\/imamci\/dnw065","type":"journal-article","created":{"date-parts":[[2016,10,25]],"date-time":"2016-10-25T11:05:33Z","timestamp":1477393533000},"page":"54-73","source":"Crossref","is-referenced-by-count":6,"title":["Polynomial matrix equivalences: system transformations and structural invariants"],"prefix":"10.1093","volume":"38","author":[{"given":"S","family":"Vologiannidis","sequence":"first","affiliation":[{"name":"Department of Informatics Engineering, Technological Educational Institute of Central Macedonia, Terma Magnisias, 62124, Serres"}]},{"given":"E N","family":"Antoniou","sequence":"additional","affiliation":[{"name":"Department of Information Technology, Alexander Technological Educational Institute of Thessaloniki, 57400 Thessaloniki, Greece"}]},{"given":"N P","family":"Karampetakis","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece"}]},{"given":"A I G","family":"Vardulakis","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece"}]}],"member":"286","published-online":{"date-parts":[[2016,12,24]]},"reference":[{"key":"2021021910180795300_B1","first-page":"194","article-title":"Strong system equivalence (i)","volume":"27","author":"Anderson","year":"(1985)","journal-title":"The ANZIAM J."},{"key":"2021021910180795300_B2","first-page":"555","article-title":"A spectral characterization of the behavior of discrete time AR-representations over a finite time interval","volume":"34","author":"Antoniou","year":"(1998)","journal-title":"Kybernetika"},{"key":"2021021910180795300_B3","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1080\/00207178108922932","article-title":"Realizations in generalized state-space form for polynomial system matrices and the definitions of poles, zeros and decoupling zeros at infinity","volume":"33","author":"Bosgra","year":"(1981)","journal-title":"Int. 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