{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T23:34:42Z","timestamp":1763681682109,"version":"3.45.0"},"reference-count":16,"publisher":"Oxford University Press (OUP)","issue":"6","license":[{"start":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T00:00:00Z","timestamp":1763596800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,11,25]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Motivated by the most recent literature, in this paper, we define a new generalization of the Frank matrix that we will call the geometric Frank matrix. In addition to considering some of its algebraic properties, we obtain its $LU$ factorization, its determinant, as well as a recurrence relation for its permanent. Upper bounds are set for the spectral norm. We also investigate similar properties for the Hadamard inverse of the geometric Frank matrix. Finally, we provide a MATLAB-R2023a code to facilitate the computation of the permanent of an arbitrary geometric Frank matrix.<\/jats:p>","DOI":"10.1093\/jigpal\/jzaf039","type":"journal-article","created":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T08:07:36Z","timestamp":1747210056000},"source":"Crossref","is-referenced-by-count":0,"title":["A new extension of the Frank matrix and its properties"],"prefix":"10.1093","volume":"33","author":[{"given":"Samet","family":"Arpaci","sequence":"first","affiliation":[{"name":"Department of Mathematics , Ankara Ha\u0131 Bayram Veli University, Ankara, 06900, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fatih","family":"Yilmaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics , Ankara Ha\u0131 Bayram Veli University, Ankara, 06900, 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