{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T12:11:05Z","timestamp":1761826265865,"version":"build-2065373602"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Port. Math."],"published-print":{"date-parts":[[2007,6,30]]},"abstract":"<jats:p>\n                    A canonical form under congruence for nonsingular complex matrices may be deduced from the canonical pair form for Hermitian matrices in a straightforward way. This allows the study of\n                    <jats:inline-formula>\n                      <jats:tex-math>A^{-1}A^*<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    and what it says about the congruence class of\n                    <jats:inline-formula>\n                      <jats:tex-math>A<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . In turn, alternate congruential forms may be given along with a further generalization of Sylvester's law of inertia and an application to C-S equivalence.\n                  <\/jats:p>","DOI":"10.4171\/pm\/1785","type":"journal-article","created":{"date-parts":[[2009,12,22]],"date-time":"2009-12-22T19:14:17Z","timestamp":1261509257000},"page":"237-251","source":"Crossref","is-referenced-by-count":2,"title":["Congruence and $A^{-1}A^*$"],"prefix":"10.4171","volume":"64","author":[{"given":"Susana","family":"Furtado","sequence":"first","affiliation":[{"name":"Universidade do Porto, Portugal"}]},{"given":"Charles R.","family":"Johnson","sequence":"additional","affiliation":[{"name":"College of William and Mary, Williamsburg, United States"}]}],"member":"2673","container-title":["Portugaliae Mathematica"],"original-title":[],"link":[{"URL":"http:\/\/www.ems-ph.org\/fulltext\/10.4171\/PM\/1785","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T12:06:41Z","timestamp":1761826001000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/pm\/1785"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,6,30]]},"references-count":0,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.4171\/pm\/1785","relation":{},"ISSN":["0032-5155","1662-2758"],"issn-type":[{"type":"print","value":"0032-5155"},{"type":"electronic","value":"1662-2758"}],"subject":[],"published":{"date-parts":[[2007,6,30]]}}}