{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T13:16:09Z","timestamp":1770815769630,"version":"3.50.1"},"reference-count":59,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T00:00:00Z","timestamp":1694476800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T00:00:00Z","timestamp":1694476800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2023,10]]},"DOI":"10.1007\/s12190-023-01916-1","type":"journal-article","created":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T07:02:12Z","timestamp":1694502132000},"page":"4069-4089","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A coupled quaternion matrix equations with applications"],"prefix":"10.1007","volume":"69","author":[{"given":"Long-Sheng","family":"Liu","sequence":"first","affiliation":[]},{"given":"Shuo","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,9,12]]},"reference":[{"issue":"1\u20133","key":"1916_CR1","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1007\/s10957-021-01906-y","volume":"193","author":"L Qi","year":"2022","unstructured":"Qi, L., Luo, Z.Y., Wang, Q.W., Zhang, X.Z.: Quaternion matrix optimization: motivation and analysis. J. Optim. Theory Appl. 193(1\u20133), 621\u2013648 (2022)","journal-title":"J. Optim. Theory Appl."},{"key":"1916_CR2","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/j.sigpro.2010.06.024","volume":"91","author":"CC Took","year":"2011","unstructured":"Took, C.C., Mandic, D.P.: Augmented second-order statistics of quaternion random signals. Signal Process. 91, 214\u2013224 (2011)","journal-title":"Signal Process."},{"key":"1916_CR3","doi-asserted-by":"crossref","unstructured":"Jia, Z.G., Ling, S.T., Zhao, M.X.: Color two-dimensional principal component analysis for face recognition based on quaternion model. In: Proceedings of the International Conference on Intelligent Computing: Intelligent Computing Theories and Application. Liverpool, UK, 7-10 August (2017) pp. 177-189","DOI":"10.1007\/978-3-319-63309-1_17"},{"issue":"1","key":"1916_CR4","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/s00006-021-01195-8","volume":"32","author":"ZH He","year":"2022","unstructured":"He, Z.H., Navasca, C., Wang, X.X.: Decomposition for a quaternion tensor triplet with applications. Adv. Appl. Clifford Algebras 32(1), 9 (2022)","journal-title":"Adv. Appl. Clifford Algebras"},{"issue":"6","key":"1916_CR5","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s40314-021-01579-3","volume":"40","author":"ZH He","year":"2021","unstructured":"He, Z.H., Qin, W.L., Wang, X.X.: Some applications of a decomposition for five quaternion matrices in control system and color image processing. Comput. Appl. Math. 40(6), 205 (2021)","journal-title":"Comput. Appl. Math."},{"issue":"3","key":"1916_CR6","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1142\/S0219530520400084","volume":"19","author":"ZH He","year":"2021","unstructured":"He, Z.H., Chen, C., Wang, X.X.: A simultaneous decomposition for three quaternion tensors with applications in color video signal processing. Anal. Appl. 19(3), 529\u2013549 (2021)","journal-title":"Anal. Appl."},{"key":"1916_CR7","doi-asserted-by":"crossref","first-page":"113494","DOI":"10.1016\/j.cam.2021.113494","volume":"393","author":"SW Yu","year":"2021","unstructured":"Yu, S.W., He, Z.H., Qi, T.C., Wang, X.X.: The equivalence canonical form of five quaternion matrices with applications to imaging and Sylvester-type equations. J. Comput. Appl. Math. 393, 113494 (2021)","journal-title":"J. Comput. Appl. Math."},{"issue":"3","key":"1916_CR8","first-page":"692","volume":"14","author":"ZH He","year":"2021","unstructured":"He, Z.H., Ng Michael, K., Zeng, C.: Generalized singular value decompositions for tensors and their applications. Numer. Math-Theory Me. 14(3), 692\u2013713 (2021)","journal-title":"Numer. Math-Theory Me."},{"key":"1916_CR9","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.cam.2018.09.001","volume":"349","author":"ZH He","year":"2019","unstructured":"He, Z.H., Wang, Q.W., Zhang, Y.: A simultaneous decomposition for seven matrices with applications. J. Comput. Appl. Math. 349, 93\u2013113 (2019)","journal-title":"J. Comput. Appl. Math."},{"key":"1916_CR10","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.sysconle.2004.07.002","volume":"54","author":"EB Castelan","year":"2005","unstructured":"Castelan, E.B., da Silva, V.G.: On the solution of a Sylvester equation appearing in descriptor systems control theory. Syst. Control Lett. 54, 109\u2013117 (2005)","journal-title":"Syst. Control Lett."},{"key":"1916_CR11","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1109\/TNN.2002.1031938","volume":"13","author":"YN Zhang","year":"2002","unstructured":"Zhang, Y.N., Jiang, D.C., Wang, J.: A recurrent neural network for solving Sylvester equation with time-varying coefficients. IEEE Trans. Neural Netw. 13, 1053\u20131063 (2002)","journal-title":"IEEE Trans. Neural Netw."},{"key":"1916_CR12","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1109\/9.210155","volume":"38","author":"VL Syrmos","year":"1993","unstructured":"Syrmos, V.L., Lewis, F.L.: Output feedback eigenstructure assignment using two Sylvester equations. IEEE Trans. Autom. Control 38, 495\u2013499 (1993)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"2","key":"1916_CR13","doi-asserted-by":"crossref","first-page":"580","DOI":"10.1137\/151005907","volume":"36","author":"A Dmytryshyn","year":"2015","unstructured":"Dmytryshyn, A., K\u0227gstr\u00f6m, B.: Coupled Sylvester-type matrix equations and block diagonalization. SIAM J. Math. Anal. 36(2), 580\u2013593 (2015)","journal-title":"SIAM J. Math. Anal."},{"key":"1916_CR14","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.laa.2012.07.049","volume":"438","author":"I Kyrchei","year":"2018","unstructured":"Kyrchei, I.: Explicit representation formulas for the minimum norm least squares solutions of some quaternion matrix equations. Linear Algebra Appl. 438, 136\u2013152 (2018)","journal-title":"Linear Algebra Appl."},{"key":"1916_CR15","first-page":"193","volume":"238","author":"I Kyrchei","year":"2014","unstructured":"Kyrchei, I.: Determinantal representations of the Drazin inverse over the quaternion skew field with applications to some matrix equations. Appl. Math. Comput. 238, 193\u2013207 (2014)","journal-title":"Appl. Math. Comput."},{"key":"1916_CR16","doi-asserted-by":"crossref","first-page":"1758","DOI":"10.3390\/math10101758","volume":"10","author":"LS Liu","year":"2022","unstructured":"Liu, L.S., Wang, Q.W., Mehany, M.S.: A Sylvester-type matrix equation over the Hamilton quaternions with an application. Mathematics 10, 1758 (2022)","journal-title":"Mathematics"},{"key":"1916_CR17","first-page":"1","volume":"64","author":"X Liu","year":"2019","unstructured":"Liu, X., Zhang, Y.: Consistency of split quaternion matrix equations $$AX^{\\star }-XB=CY+D$$ and $$X-AX^{\\star }B=CY+D$$. Adv. Appl. Clifford Algebras 64, 1\u201320 (2019)","journal-title":"Adv. Appl. Clifford Algebras"},{"key":"1916_CR18","volume-title":"Generalized Inverse: Theory and Applications","author":"A Ben-Israel","year":"1974","unstructured":"Ben-Israel, A., Greville, T.N.E.: Generalized Inverse: Theory and Applications. John Wiley and Sons, New York, NY, USA (1974)"},{"issue":"6","key":"1916_CR19","first-page":"60","volume":"20","author":"ZY Peng","year":"2003","unstructured":"Peng, Z.Y.: The centro-symmetric solutions of linear matrix equation $$AXB=C$$ and its optimal approximation. Chinese J. Eng. Math. 20(6), 60\u201364 (2003)","journal-title":"Chinese J. Eng. Math."},{"issue":"2","key":"1916_CR20","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.cam.2006.12.005","volume":"212","author":"GX Huang","year":"2008","unstructured":"Huang, G.X., Yin, F., Guo, K.: An iterative method for the skew-symmetric solution and the optimal approximate solution of the matrix equation $$AXB=C$$. J. Comput. Appl. Math. 212(2), 231\u2013244 (2008)","journal-title":"J. Comput. Appl. Math."},{"key":"1916_CR21","doi-asserted-by":"crossref","first-page":"e2245","DOI":"10.1002\/nla.2245","volume":"26","author":"ZG Jia","year":"2019","unstructured":"Jia, Z.G., Ng, M.K., Song, G.J.: Robust quaternion matrix completion with applications to image inpainting. Numer. Linear Algebra Appl. 26, e2245 (2019)","journal-title":"Numer. Linear Algebra Appl."},{"key":"1916_CR22","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.cam.2018.04.019","volume":"343","author":"ZG Jia","year":"2018","unstructured":"Jia, Z.G., Wei, M.S., Zhao, M.X., Chen, Y.: A new real structure-preserving quaternion QR algorithm. J. Comput. Appl. Math. 343, 26\u201348 (2018)","journal-title":"J. Comput. Appl. Math."},{"key":"1916_CR23","doi-asserted-by":"crossref","unstructured":"Rodman, L.: Topics in Quaternion Linear Algebra, Princeton University Press: Princeton, NJ, USA (2014)","DOI":"10.23943\/princeton\/9780691161853.001.0001"},{"key":"1916_CR24","doi-asserted-by":"crossref","first-page":"113494","DOI":"10.1016\/j.cam.2021.113494","volume":"393","author":"SW Yu","year":"2021","unstructured":"Yu, S.W., He, Z.H., Qi, T.C., Wang, X.X.: The equivalence canonical form of five quaternion matrices with applications to imaging and Sylvester-type equations. J. Comput. Appl. Math. 393, 113494 (2021)","journal-title":"J. Comput. Appl. Math."},{"key":"1916_CR25","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.amc.2013.05.069","volume":"221","author":"SF Yuan","year":"2013","unstructured":"Yuan, S.F., Wang, Q.W., Duan, X.F.: On solutions of the quaternion matrix equation $$AX=B$$ and their applications in color image restoration. J. Comput. Appl. Math. 221, 10\u201320 (2013)","journal-title":"J. Comput. Appl. Math."},{"key":"1916_CR26","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1080\/03081087.2012.703192","volume":"61","author":"ZH He","year":"2013","unstructured":"He, Z.H., Wang, Q.W.: A real quaternion matrix equation with with applications. Linear Multilinear Algebra 61, 725\u2013740 (2013)","journal-title":"Linear Multilinear Algebra"},{"key":"1916_CR27","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.automatica.2017.09.008","volume":"87","author":"ZH He","year":"2018","unstructured":"He, Z.H., Wang, Q.W., Zhang, Y.: A system of quaternary coupled Sylvester-type real quaternion matrix equations. Automatica 87, 25\u201331 (2018)","journal-title":"Automatica"},{"key":"1916_CR28","first-page":"13","volume":"298","author":"ZH He","year":"2017","unstructured":"He, Z.H., Wang, Q.W., Zhang, Y.: Simultaneous decomposition of quaternion matrices involving $$\\eta $$-Hermicity with applications. Appl. Math. Comput. 298, 13\u201335 (2017)","journal-title":"Appl. Math. Comput."},{"key":"1916_CR29","doi-asserted-by":"publisher","DOI":"10.1007\/s43037-023-00262-5","author":"XY Chen","year":"2023","unstructured":"Chen, X.Y., Wang, Q.W.: The $$\\eta $$-(anti-)Hermitian solution to a constrained Sylvester-type generalized commutative quaternion matrix equation. Banach J. Math. Anal. (2023). https:\/\/doi.org\/10.1007\/s43037-023-00262-5","journal-title":"Banach J. Math. Anal."},{"key":"1916_CR30","doi-asserted-by":"publisher","DOI":"10.1007\/s43034-023-00276-y","author":"XL Xu","year":"2023","unstructured":"Xu, X.L., Wang, Q.W.: The consistency and the general common solution to some quaternion matrix equations. Ann. Funct. Anal. (2023). https:\/\/doi.org\/10.1007\/s43034-023-00276-y","journal-title":"Ann. Funct. Anal."},{"issue":"9","key":"1916_CR31","doi-asserted-by":"publisher","first-page":"2731","DOI":"10.2298\/FIL2309731L","volume":"37","author":"LS Liu","year":"2023","unstructured":"Liu, L.S., Wang, Q.W.: The reducible solution to a system of matrix equations over the Hamilton quaternion algebra. Filomat 37(9), 2731\u201342 (2023). https:\/\/doi.org\/10.2298\/FIL2309731L","journal-title":"Filomat"},{"key":"1916_CR32","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/s00006-021-01122-x","volume":"31","author":"ZH He","year":"2021","unstructured":"He, Z.H., Wang, M.: A quaternion matrix equation with two different restrictions. Adv. Appl. Clifford Algebras 31, 25 (2021)","journal-title":"Adv. Appl. Clifford Algebras"},{"key":"1916_CR33","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1016\/j.laa.2016.02.013","volume":"496","author":"ZH He","year":"2016","unstructured":"He, Z.H., Agudelo, O.M., Wang, Q.W., De Moor, B.: Two-sided coupled generalized sylvester matrix equations solving using a simultaneous decomposition for fifteen matrices. Linear Algebra Appl. 496, 549\u2013593 (2016)","journal-title":"Linear Algebra Appl."},{"issue":"2","key":"1916_CR34","doi-asserted-by":"crossref","first-page":"375","DOI":"10.3390\/sym14020375","volume":"14","author":"LS Liu","year":"2022","unstructured":"Liu, L.S., Wang, Q.W., Chen, J.F., Xie, Y.Z.: An exact solution to a quaternion matrix equation with an application. Symmetry 14(2), 375 (2022)","journal-title":"Symmetry"},{"key":"1916_CR35","doi-asserted-by":"crossref","first-page":"1056","DOI":"10.3390\/sym14051056","volume":"14","author":"RN Wang","year":"2022","unstructured":"Wang, R.N., Wang, Q.W., Liu, L.S.: Solving a system of Sylvester-like quaternion matrix equations. Symmetry 14, 1056 (2022)","journal-title":"Symmetry"},{"key":"1916_CR36","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.automatica.2016.02.024","volume":"69","author":"QW Wang","year":"2016","unstructured":"Wang, Q.W., Rehman, A., He, Z.H., Zhang, Y.: Constraint generalized Sylvester matrix equations. Automatica 69, 60\u201364 (2016)","journal-title":"Automatica"},{"key":"1916_CR37","doi-asserted-by":"crossref","first-page":"2840","DOI":"10.1016\/j.automatica.2014.10.033","volume":"50","author":"QW Wang","year":"2014","unstructured":"Wang, Q.W., He, Z.H.: Systems of coupled generalized Sylvester matrix equations. Automatica 50, 2840\u20132844 (2014)","journal-title":"Automatica"},{"key":"1916_CR38","doi-asserted-by":"crossref","first-page":"2713","DOI":"10.1016\/j.automatica.2013.06.009","volume":"49","author":"QW Wang","year":"2013","unstructured":"Wang, Q.W., He, Z.H.: Solvability conditions and general solution for mixed Sylvester equations. Automatica 49, 2713\u20132719 (2013)","journal-title":"Automatica"},{"key":"1916_CR39","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/j.automatica.2018.12.001","volume":"101","author":"QW Wang","year":"2019","unstructured":"Wang, Q.W., He, Z.H., Zhang, Y.: Constrained two-side coupled Sylvester-type quaternion matrix equations. Automatica 101, 207\u2013213 (2019)","journal-title":"Automatica"},{"key":"1916_CR40","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1007\/s40314-022-01873-8","volume":"41","author":"YF Xu","year":"2022","unstructured":"Xu, Y.F., Wang, Q.W., Liu, L.S., Mehany, M.S.: A constrained system of matrix equations. Comp. Appl. Math. 41, 166 (2022)","journal-title":"Comp. Appl. Math."},{"issue":"16","key":"1916_CR41","doi-asserted-by":"crossref","first-page":"3069","DOI":"10.1080\/03081087.2019.1704213","volume":"69","author":"ZH He","year":"2021","unstructured":"He, Z.H.: Some new results on a system of Sylvester-type quaternion matrix equations. Linear Multilinear Algebra 69(16), 3069\u20133091 (2021)","journal-title":"Linear Multilinear Algebra"},{"issue":"18","key":"1916_CR42","doi-asserted-by":"crossref","first-page":"14274","DOI":"10.1002\/mma.7696","volume":"44","author":"ZH He","year":"2021","unstructured":"He, Z.H., Wang, M.: Solvability conditions and general solutions to some quaternion matrix equations. Math. Method. Appl. Sci. 44(18), 14274\u201314291 (2021)","journal-title":"Math. Method. Appl. Sci."},{"key":"1916_CR43","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.automatica.2017.09.008","volume":"87","author":"ZH He","year":"2018","unstructured":"He, Z.H., Wang, Q.W., Zhang, Y.: A system of quaternary coupled Sylvester-type real quaternion matrix equations. Automatica 87, 25\u201331 (2018)","journal-title":"Automatica"},{"key":"1916_CR44","doi-asserted-by":"crossref","first-page":"475","DOI":"10.13001\/1081-3810.3606","volume":"32","author":"ZH He","year":"2017","unstructured":"He, Z.H., Liu, J.Z., Tam, T.Y.: The general $$\\phi $$-hermitian solution to mixed pairs of quaternion matrix Sylvester equations. Electron. J. Linear Al. 32, 475\u2013499 (2017)","journal-title":"Electron. J. Linear Al."},{"key":"1916_CR45","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/s00006-021-01122-x","volume":"31","author":"ZH He","year":"2021","unstructured":"He, Z.H., Wang, M.: A quaternion matrix equation with two different restrictions. Adv. Appl. Clifford Algebras 31, 25 (2021)","journal-title":"Adv. Appl. Clifford Algebras"},{"key":"1916_CR46","doi-asserted-by":"crossref","first-page":"2017","DOI":"10.1080\/03081087.2014.896361","volume":"63","author":"ZH He","year":"2015","unstructured":"He, Z.H., Wang, Q.W.: The general solutions to some systems of matrix equations. Linear Multilinear Algebra 63, 2017\u20132032 (2015)","journal-title":"Linear Multilinear Algebra"},{"issue":"5","key":"1916_CR47","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1007\/s00006-018-0909-0","volume":"28","author":"I Kyrchei","year":"2018","unstructured":"Kyrchei, I.: Cramer\u2019s rules for Sylvester quaternion matrix equation and its special cases. Adv. Appl. Clifford Algebras 28(5), 90 (2018)","journal-title":"Adv. Appl. Clifford Algebras"},{"issue":"3","key":"1916_CR48","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1007\/s00006-019-0972-1","volume":"29","author":"I Kyrchei","year":"2019","unstructured":"Kyrchei, I.: Cramer\u2019s rules of $$\\eta $$-(skew-) Hermitian solutions to the quaternion Sylvester-type matrix equations. Adv. Appl. Clifford Algebras 29(3), 56 (2019)","journal-title":"Adv. Appl. Clifford Algebras"},{"issue":"5","key":"1916_CR49","doi-asserted-by":"crossref","first-page":"1047","DOI":"10.1007\/s11464-020-0865-6","volume":"15","author":"MY Xie","year":"2020","unstructured":"Xie, M.Y., Wang, Q.W.: The reducible solution to a quaternion tensor equation. Front. Math. China 15(5), 1047\u20131070 (2020)","journal-title":"Front. Math. China"},{"key":"1916_CR50","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4471-3037-6","volume-title":"Optimal Sampled-data Control Systems","author":"T Chen","year":"1995","unstructured":"Chen, T., Francis, B.A.: Optimal Sampled-data Control Systems. Springer, London (1995)"},{"key":"1916_CR51","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1137\/0131050","volume":"31","author":"CG Khatri","year":"1976","unstructured":"Khatri, C.G., Mitra, S.K.: Hermitian and nonnegative definite solutions of linear matrix equations. SIAM J. Appl. Math. 31, 579\u2013585 (1976)","journal-title":"SIAM J. Appl. Math."},{"key":"1916_CR52","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.laa.2008.01.030","volume":"429","author":"QX Xu","year":"2008","unstructured":"Xu, Q.X.: Common hermitian and positive solutions to the adjointable operator equations $$AX=C, XB=D$$. Linear Algebra Appl. 429, 1\u201311 (2008)","journal-title":"Linear Algebra Appl."},{"key":"1916_CR53","first-page":"57","volume":"21","author":"J Gr\u00f6\u00df","year":"1998","unstructured":"Gr\u00f6\u00df, J.: A note on the general Hermitian solution to $$AXA^{*}=B$$. Bull. Malays. Math. Soc. 21, 57\u201362 (1998)","journal-title":"Bull. Malays. Math. Soc."},{"key":"1916_CR54","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/S0024-3795(00)00033-1","volume":"321","author":"J Gr\u00f6\u00df","year":"2000","unstructured":"Gr\u00f6\u00df, J.: Nonnegative-definite and positive-definite solutions to the matrix equation $$AXA^{*}=B$$ revisited. Linear Algebra Appl. 321, 123\u2013129 (2000)","journal-title":"Linear Algebra Appl."},{"key":"1916_CR55","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1080\/03081080701248112","volume":"55","author":"DS Cvetkovi\u0107\u0107-IIi\u0107","year":"2007","unstructured":"Cvetkovi\u0107\u0107-IIi\u0107, D.S., Daji\u0107, A., Koliha, J.J.: Positive and real-positive solutions to the equation $$axa^{*}=c$$ in $$C^{*}$$-algebras. Linear Multilinear Algebra 55, 535\u2013543 (2007)","journal-title":"Linear Multilinear Algebra"},{"key":"1916_CR56","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1080\/03081087408817070","volume":"2","author":"G Marsaglia","year":"1974","unstructured":"Marsaglia, G., Styan, G.P.: Equalities and inequalities for ranks of matrices. Linear Multilinear Algebra 2, 269\u2013292 (1974)","journal-title":"Linear Multilinear Algebra"},{"key":"1916_CR57","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/0024-3795(79)90004-1","volume":"25","author":"JK Baksalary","year":"1979","unstructured":"Baksalary, J.K., Kala, R.: The matrix equations $$AX-YB=C$$. Linear Algebra Appl. 25, 41\u201343 (1979)","journal-title":"Linear Algebra Appl."},{"key":"1916_CR58","first-page":"404","volume":"38","author":"P Bhimasankaram","year":"1976","unstructured":"Bhimasankaram, P.: Common solutions to the linear matrix equations $$AX=C$$, $$XB=D$$ and $$FXG=H$$. Sankhya Ser. A 38, 404\u2013409 (1976)","journal-title":"Sankhya Ser. A"},{"issue":"3","key":"1916_CR59","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1017\/S0305004100030401","volume":"51","author":"R Penrose","year":"1955","unstructured":"Penrose, R.: A generalized inverse for matrices. Proc. Camb. Philos. Soc. 51(3), 406\u2013413 (1955)","journal-title":"Proc. Camb. Philos. Soc."}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-023-01916-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-023-01916-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-023-01916-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T14:35:33Z","timestamp":1695825333000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-023-01916-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,12]]},"references-count":59,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2023,10]]}},"alternative-id":["1916"],"URL":"https:\/\/doi.org\/10.1007\/s12190-023-01916-1","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9,12]]},"assertion":[{"value":"12 May 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 August 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 August 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 September 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}