{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:29:07Z","timestamp":1787336947225,"version":"build-2736575974"},"reference-count":12,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2003,1]]},"abstract":"<jats:p>\n                    Let A and K be real symmetric matrices with K\n                    <jats:sup>2<\/jats:sup>\n                    =I. In the article \"A spectral characterization of generalized real symmetric centrosymmetric and generalized real symmetric skew-centrosymmetric matrices\" [D. Tao and M. Yasuda, SIAM J. Matrix Anal. Appl., 23 (2002), pp. 885--895], it was shown that (1) AK=KA if and only if the spectrum of A equals the spectrum of KA up to sign and (2) AK=-KA if and only if the spectrum of A equals the spectrum of KA multiplied by i. This paper extends these spectral characterizations from the case of real symmetric matrices to that of self-adjoint compact linear operators in a complex Hilbert space. Some consequences of these results are mentioned, including an application that describes the correspondence between the spectrum of a real symmetric Toeplitz matrix T and its associated Hankel matrix JT, where J is the so-called exchange matrix.\n                  <\/jats:p>","DOI":"10.1137\/s0895479802418835","type":"journal-article","created":{"date-parts":[[2003,12,22]],"date-time":"2003-12-22T21:00:49Z","timestamp":1072126849000},"page":"601-605","source":"Crossref","is-referenced-by-count":22,"title":["Spectral Characterizations for Hermitian Centrosymmetric\n                    <i>K<\/i>\n                    -Matrices and Hermitian Skew-Centrosymmetric\n                    <i>K<\/i>\n                    -Matrices"],"prefix":"10.1137","volume":"25","author":[{"given":"Mark","family":"Yasuda","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(73)90049-9"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1109\/TASSP.1985.1164644"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144597328341"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(76)90101-4"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479895288759"},{"key":"R6","doi-asserted-by":"crossref","unstructured":"I. Gohberg and M. Krein,\n                      Introduction to the Theory of Linear Nonselfadjoint Operators\n                      , Transl. Math. Monogr. 18, AMS, Providence, RI, 1969.","DOI":"10.1090\/mmono\/018"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(92)90167-9"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511810817"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"R. Kadison and J. Ringrose,\n                      Fundamentals of the Theory of Operator Algebras\n                      , AMS, Providence, RI, 1997.","DOI":"10.1090\/gsm\/015"},{"key":"R10","unstructured":"K. McClanahan,\n                      personal correspondence\n                      , 2002."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479801386730"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(83)90138-6"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0895479802418835","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:37:51Z","timestamp":1787333871000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0895479802418835"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,1]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2003,1]]}},"alternative-id":["10.1137\/S0895479802418835"],"URL":"https:\/\/doi.org\/10.1137\/s0895479802418835","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,1]]}}}