caa a22 4500 445830603 CHVBK 20180317145314.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s10255-011-0083-9 doi (NATIONALLICENCE)springer-10.1007/s10255-011-0083-9 Ranks of the common solution to six quaternion matrix equations [Elektronische Daten] [Qing-wen Wang, Yan Zhou, Qin Zhang] A new expression is established for the common solution to six classical linear quaternion matrix equations A 1 X = C 1, XB 1 = C 3, A 2 X = C 2, XB 2 = C 4, A 3 XB 3 = C 5, A 4 XB 4 = C 6 which was investigated recently by Wang, Chang and Ning (Q. Wang, H. Chang, Q. Ning, The common solution to six quaternion matrix equations with applications, Appl. Math. Comput. 195: 721-732 (2008)). Formulas are derived for the maximal and minimal ranks of the common solution to this system. Moreover, corresponding results on some special cases are presented. As an application, a necessary and sufficient condition is presented for the invariance of the rank of the general solution to this system. Some known results can be regarded as the special cases of the results in this paper. Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg, 2011 system of matrix equations nationallicence quaternion matrix nationallicence minimal rank nationallicence maximal rank nationallicence linear matrix expression nationallicence generalized inverse nationallicence Wang Qing-wen Department of Mathematics, Shanghai University, 99 Shangda Road, 200444, Shanghai, China aut Zhou Yan Department of Mathematics, Shanghai University, 99 Shangda Road, 200444, Shanghai, China aut Zhang Qin Department of Mathematics, Shanghai University, 99 Shangda Road, 200444, Shanghai, China aut Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/3(2011-07-01), 443-462 0168-9673 27:3<443 2011 27 10255 https://doi.org/10.1007/s10255-011-0083-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10255-011-0083-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Wang Qing-wen Department of Mathematics, Shanghai University, 99 Shangda Road, 200444, Shanghai, China aut NATIONALLICENCE 700 1- Zhou Yan Department of Mathematics, Shanghai University, 99 Shangda Road, 200444, Shanghai, China aut NATIONALLICENCE 700 1- Zhang Qin Department of Mathematics, Shanghai University, 99 Shangda Road, 200444, Shanghai, China aut NATIONALLICENCE 773 0- Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/3(2011-07-01), 443-462 0168-9673 27:3<443 2011 27 10255 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer