{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:30:21Z","timestamp":1787337021556,"version":"build-2736575974"},"reference-count":11,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2003,1]]},"abstract":"<jats:p>New factorization results dealing mainly with P-matrices and M-matrices are presented. It is proved that any matrix in $M_n (\\mathbb{R})$ with positive determinant can be written as the product of three P-matrices (compared with the classical result that five positive definite matrices may be needed). It is also proved that a matrix A with positive determinant can be stabilized via multiplication by a P-matrix if and only if A is not a diagonal matrix with all diagonal entries negative. Factorization into two P-matrices is considered and characterized for n=2. Using elementary bidiagonal factorization results, it is shown that the nonsingular M-matrices, or the nonsingular totally nonnegative matrices, generate all matrices in $M_n (\\mathbb{R})$ with positive determinant. Further results on products of M-matrices and inverse M-matrices are given. (A correction to this article has been appended to the pdf file.)<\/jats:p>","DOI":"10.1137\/s0895479802418446","type":"journal-article","created":{"date-parts":[[2003,7,12]],"date-time":"2003-07-12T09:30:34Z","timestamp":1058002234000},"page":"285-294","source":"Crossref","is-referenced-by-count":3,"title":["Matrix Classes That Generate All Matrices with Positive Determinant"],"prefix":"10.1137","volume":"25","author":[{"given":"C. R.","family":"Johnson","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"D. D.","family":"Olesky","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P.","family":"van den Driessche","sequence":"additional","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(87)90313-2"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(68)90093-8"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1970-0260765-X"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1080\/03081087508817108"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-092250-5.50009-6"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100002978"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511810817"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511840371"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1080\/03081088408817607"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(99)00037-3"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1080\/03081088608817711"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0895479802418446","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:41:10Z","timestamp":1787334070000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0895479802418446"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,1]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2003,1]]}},"alternative-id":["10.1137\/S0895479802418446"],"URL":"https:\/\/doi.org\/10.1137\/s0895479802418446","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,1]]}}}