{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T06:50:27Z","timestamp":1783493427195,"version":"3.55.0"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2007,7,18]],"date-time":"2007-07-18T00:00:00Z","timestamp":1184716800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2009,3]]},"DOI":"10.1007\/s10107-007-0159-8","type":"journal-article","created":{"date-parts":[[2007,7,17]],"date-time":"2007-07-17T11:23:09Z","timestamp":1184671389000},"page":"195-221","source":"Crossref","is-referenced-by-count":52,"title":["Z-transformations on proper and symmetric cones"],"prefix":"10.1007","volume":"117","author":[{"given":"M. Seetharama","family":"Gowda","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiyuan","family":"Tao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2007,7,18]]},"reference":[{"key":"159_CR1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511529979","volume-title":"Nonnegative Matrices and Applications","author":"R.B. Bapat","year":"1997","unstructured":"Bapat R.B., Raghavan T.E.S. (1997). Nonnegative Matrices and Applications. Cambridge University Press, Cambridge"},{"key":"159_CR2","volume-title":"Nonnegative Matrices in Dynamical Systems","author":"A. Berman","year":"1989","unstructured":"Berman A., Neumann M., Stern R.J. (1989). Nonnegative Matrices in Dynamical Systems. Wiley, New York"},{"key":"159_CR3","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611971262","volume-title":"Nonnegative Matrices in the Mathematical Sciences","author":"A. Berman","year":"1994","unstructured":"Berman A., Plemmons R.J. (1994). Nonnegative Matrices in the Mathematical Sciences. SIAM, Philadelphia"},{"key":"159_CR4","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1287\/moor.14.3.534","volume":"14","author":"J.M. Borwein","year":"1989","unstructured":"Borwein J.M., Dempster M.A.H. (1989). The order linear complementarity problem. Math. Oper. Res. 14: 534\u2013558","journal-title":"Math. Oper. Res."},{"key":"159_CR5","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970777","volume-title":"Linear Matrix Inequalities in System and Control Theory","author":"S. Boyd","year":"1994","unstructured":"Boyd S., El Ghaoui L., Feron E., Balakrishnan V. (1994). Linear Matrix Inequalities in System and Control Theory. SIAM publications, Philadelphia"},{"key":"159_CR6","volume-title":"The Linear Complementarity Problem","author":"R.W. Cottle","year":"1992","unstructured":"Cottle R.W., Pang J.-S., Stone R.E. (1992). The Linear Complementarity Problem. Academic, Boston"},{"key":"159_CR7","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1137\/0318005","volume":"18","author":"C.W. Cryer","year":"1980","unstructured":"Cryer C.W., Dempster M.A.H. (1980). Equivalence of linear complementarity and linear programs in vector lattice Hilbert spaces. SIAM J. Control Optim. 18: 76\u201390","journal-title":"SIAM J. Control Optim."},{"key":"159_CR8","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.laa.2003.12.045","volume":"393","author":"T. Damm","year":"2004","unstructured":"Damm T. (2004). Positive groups on H n are completely positive. Linear Algebra Appl. 393: 127\u2013137","journal-title":"Linear Algebra Appl."},{"key":"159_CR9","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/0024-3795(74)90070-6","volume":"8","author":"L. Elsner","year":"1974","unstructured":"Elsner L. (1974). Quasimonotonie and ungleischungen in halbgeordneten R\u00e4umen. Linear Algebra Appl. 8: 249\u2013261","journal-title":"Linear Algebra Appl."},{"key":"159_CR10","volume-title":"Finite Dimensional Variational Inequalities and Complementarity Problems","author":"F. Facchinei","year":"2003","unstructured":"Facchinei F., Pang J.-S. (2003). Finite Dimensional Variational Inequalities and Complementarity Problems. Springer, New York"},{"key":"159_CR11","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198534778.001.0001","volume-title":"Analysis on Symmetric Cones","author":"J. Faraut","year":"1994","unstructured":"Faraut J., Kor\u00e1nyi A. (1994). Analysis on Symmetric Cones. Oxford University Press, Oxford"},{"key":"159_CR12","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1007\/BF01696240","volume":"12","author":"M. Fiedler","year":"1962","unstructured":"Fiedler M., Pt\u00e1k V. (1962). On matrices with non-positive off-diagonal elements and positive principle minors. Czechoslov. Math. J. 12: 382\u2013400","journal-title":"Czechoslov. Math. J."},{"key":"159_CR13","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1007\/BF01258188","volume":"9","author":"P. Finsler","year":"1937","unstructured":"Finsler P. (1937). \u00dcber das Vorkommen definiter und semidefiniter Formen in Scharen quadratisher Formen. Comment. Math. Helv. 9: 188\u2013192","journal-title":"Comment. Math. Helv."},{"key":"159_CR14","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/S0024-3795(00)00208-1","volume":"320","author":"M.S. Gowda","year":"2000","unstructured":"Gowda M.S., Parthasarathy T. (2000). Complementarity forms of theorems of Lyapunov and Stein and related results. Linear Algebra Appl. 320: 131\u2013144","journal-title":"Linear Algebra Appl."},{"key":"159_CR15","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1007\/PL00011387","volume":"88","author":"M.S. Gowda","year":"2000","unstructured":"Gowda M.S., Song Y. (2000). On semidefinite linear complementarity problems. Math. Program. Series A 88: 575\u2013587","journal-title":"Math. Program. Series A"},{"key":"159_CR16","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1137\/S0895479800377927","volume":"24","author":"M.S. Gowda","year":"2002","unstructured":"Gowda M.S., Song Y. (2002). Some new results for the semidefinite linear complementarity problem. SIAM J. Matrix Anal. Appl. 24: 25\u201339","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"159_CR17","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/S0024-3795(03)00425-7","volume":"370","author":"M.S. Gowda","year":"2003","unstructured":"Gowda M.S., Song Y., Ravindran G. (2003). On some interconnections between strict monotonicity, globally uniquely solvable, and P properties in semidefinite linear complementarity problems. Linear Algebra Appl. 370: 355\u2013368","journal-title":"Linear Algebra Appl."},{"key":"159_CR18","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/j.laa.2004.03.028","volume":"393","author":"M.S. Gowda","year":"2004","unstructured":"Gowda M.S., Sznajder R., Tao J. (2004). Some P-properties for linear transformations on Euclidean Jordan algebras. Linear Algebra Appl. 393: 203\u2013232","journal-title":"Linear Algebra Appl."},{"key":"159_CR19","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/0024-3795(93)00364-6","volume":"223\/224","author":"P. Gritzmann","year":"1995","unstructured":"Gritzmann P., Klee V., Tam B.-S. (1995). Cross-positive matrices revisited. Linear Algebra Appl. 223\/224: 285\u2013305","journal-title":"Linear Algebra Appl."},{"key":"159_CR20","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511840371","volume-title":"Topics in Matrix Analysis","author":"R.A. Horn","year":"1991","unstructured":"Horn R.A., Johnson C.R. (1991). Topics in Matrix Analysis. Cambridge University Press, Cambridge"},{"key":"159_CR21","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/0024-3795(78)90045-9","volume":"20","author":"I. Kaneko","year":"1978","unstructured":"Kaneko I. (1978). Linear complementarity problems and characterizations of Minkowski matrices. Linear Algebra Appl. 20: 113\u2013130","journal-title":"Linear Algebra Appl."},{"key":"159_CR22","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/BF00934094","volume":"19","author":"S. Karamardian","year":"1976","unstructured":"Karamardian S. (1976). An existence theorem for the complementarity problem. Optim. Theory Appl. 19: 227\u2013232","journal-title":"Optim. Theory Appl."},{"key":"159_CR23","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1007\/PL00004442","volume":"319","author":"Y. Lim","year":"2001","unstructured":"Lim Y. (2001). Applications of geometric means on symmetric cones. Math. Ann. 319: 457\u2013468","journal-title":"Math. Ann."},{"key":"159_CR24","volume-title":"Degree Theory","author":"N.G. Lloyd","year":"1978","unstructured":"Lloyd N.G. (1978). Degree Theory. Cambridge University Press, Cambridge"},{"key":"159_CR25","doi-asserted-by":"crossref","first-page":"42","DOI":"10.13001\/1081-3810.1144","volume":"12","author":"O. Mason","year":"2005","unstructured":"Mason O., Shorten R. (2005). The geometry of convex cones associated with the Lyapunov inequality and the common Lyapunov function problem. Electron. J. Linear Algebra 12: 42\u201363","journal-title":"Electron. J. Linear Algebra"},{"key":"159_CR26","unstructured":"Mesbahi, M., Papavassilopoulos, G.P.: Least elements and the minimal rank matrices, in complementarity problems and variational problems, State of the art. In: Proceedings of the International Conference on Complementarity Problems. SIAM Publications, Philadelphia (1997)"},{"key":"159_CR27","doi-asserted-by":"crossref","first-page":"2469","DOI":"10.1109\/9.362846","volume":"39","author":"K.S. Narendra","year":"1994","unstructured":"Narendra K.S., Balakrishnan J. (1994). A common Lyapunov function for stable LTI systems with commuting A-matrices. IEEE Trans. Autom. Control 39: 2469\u20132471","journal-title":"IEEE Trans. Autom. Control"},{"key":"159_CR28","doi-asserted-by":"crossref","first-page":"1211","DOI":"10.1137\/040606557","volume":"16","author":"B.K. Rangarajan","year":"2006","unstructured":"Rangarajan B.K. (2006). Polynomial convergence of infeasible-interior-point methods over symmetric cones. SIAM J. Optim. 16: 1211\u20131229","journal-title":"SIAM J. Optim."},{"key":"159_CR29","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1287\/moor.17.3.691","volume":"17","author":"S.M. Robinson","year":"1992","unstructured":"Robinson S.M. (1992). Normal maps induced by linear transformations. Math. Oper. Res. 17: 691\u2013714","journal-title":"Math. Oper. Res."},{"key":"159_CR30","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/BF01397969","volume":"7","author":"H. Schneider","year":"1965","unstructured":"Schneider H. (1965). Positive operators and an inertia theorem. Numer. Math. 7: 11\u201317","journal-title":"Numer. Math."},{"key":"159_CR31","doi-asserted-by":"crossref","first-page":"508","DOI":"10.1137\/0707041","volume":"7","author":"H. Schneider","year":"1970","unstructured":"Schneider H., Vidyasagar M. (1970). Cross-positive matrices. SIAM J. Numer. Anal. 7: 508\u2013519","journal-title":"SIAM J. Numer. Anal."},{"key":"159_CR32","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/0024-3795(81)90099-9","volume":"41","author":"R.J. Stern","year":"1981","unstructured":"Stern R.J. (1981). Generalized M-matrices. Linear Algebra Appl. 41: 201\u2013208","journal-title":"Linear Algebra Appl."},{"key":"159_CR33","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/BF01460118","volume":"9","author":"R.J. Stern","year":"1982","unstructured":"Stern R.J. (1982). A note on positively invariant cones. Appl. Math. Optim. 9: 67\u201372","journal-title":"Appl. Math. Optim."},{"key":"159_CR34","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0024-3795(87)90134-0","volume":"97","author":"R.J. Stern","year":"1987","unstructured":"Stern R.J., Tsatsomeros M. (1987). Extended M-matrices and subtangentiality. Linear Algebra Appl. 97: 1\u201311","journal-title":"Linear Algebra Appl."},{"key":"159_CR35","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1137\/0612012","volume":"12","author":"R.J. Stern","year":"1991","unstructured":"Stern R.J., Wolkowicz H. (1991). Exponential nonnegativity on the ice-cream cone. SIAM J. Matrix Anal. 12: 160\u2013165","journal-title":"SIAM J. Matrix Anal."},{"key":"159_CR36","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1016\/j.laa.2005.11.021","volume":"416","author":"R. Sznajder","year":"2006","unstructured":"Sznajder R., Gowda M.S. (2006). The Q-property of composite transformations and the P-property of Stein-type transformations on self-dual and symmetric cones. Linear Algebra Appl. 416: 437\u2013451","journal-title":"Linear Algebra Appl."},{"key":"159_CR37","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/0024-3795(76)90014-8","volume":"15","author":"B.-S. Tam","year":"1976","unstructured":"Tam B.-S. (1976). Some results on cross-positive matrices. Linear Algebra Appl. 15: 173\u2013176","journal-title":"Linear Algebra Appl."},{"key":"159_CR38","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1287\/moor.1050.0157","volume":"30","author":"J. Tao","year":"2005","unstructured":"Tao J., Gowda M.S. (2005). Some P-properties for nonlinear transformations on Euclidean Jordan algebras. Math. Oper. Res. 30: 985\u20131004","journal-title":"Math. Oper. Res."},{"key":"159_CR39","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/0024-3795(79)90020-X","volume":"25","author":"F. Uhlig","year":"1979","unstructured":"Uhlig F. (1979). A recurring theorem about pairs of quadratic forms and extensions: a survey. Linear Algebra Appl. 25: 219\u2013237","journal-title":"Linear Algebra Appl."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-007-0159-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-007-0159-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-007-0159-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,19]],"date-time":"2025-01-19T15:02:43Z","timestamp":1737298963000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-007-0159-8"}},"subtitle":["Z-transformations"],"short-title":[],"issued":{"date-parts":[[2007,7,18]]},"references-count":39,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2009,3]]}},"alternative-id":["159"],"URL":"https:\/\/doi.org\/10.1007\/s10107-007-0159-8","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,7,18]]}}}