"The maximal and minimal ranks of matrix expression with applications", Z. Xiong, Y. Qin and S. Yuan, Journal of Inequalities and Applications 2012 2012:54
Yongge Tian, Central University of Finance and Economics, Beijing 100081, China
9 January 2013
This comment points out the following errata in the article "The maximal and minimal ranks of matrix expression with applications" by Z. Xiong et al, 2012 2012:54 of this journal:
(I) Because S1, S2, S3, S4 in (7) are different, Formulas (8)-(11) cannot necessarily hold for the same pair of matrices V1 and V2. So that it is invalid to substitute (8)-(11) into (7) simultaneously.
(II) Formulas (22)-(29) cannot necessarily hold for the same pair of matrices V1 and V2, so that it is invalid to substitute (22)-(29) into (20) simultaneously.
In view of these two facts, the main results in the article and their consequences are all wrong, while correct formulas for calculating the maximal and minimal ranks of (4) cannot be established by the method adopted in the article.
"The maximal and minimal ranks of matrix expression with applications", Z. Xiong, Y. Qin and S. Yuan, Journal of Inequalities and Applications 2012 2012:54
9 January 2013
This comment points out the following errata in the article "The maximal and minimal ranks of matrix expression with applications" by Z. Xiong et al, 2012 2012:54 of this journal:
(I) Because S1, S2, S3, S4 in (7) are different, Formulas (8)-(11) cannot necessarily hold for the same pair of matrices V1 and V2. So that it is invalid to substitute (8)-(11) into (7) simultaneously.
(II) Formulas (22)-(29) cannot necessarily hold for the same pair of matrices V1 and V2, so that it is invalid to substitute (22)-(29) into (20) simultaneously.
In view of these two facts, the main results in the article and their consequences are all wrong, while correct formulas for calculating the maximal and minimal ranks of (4) cannot be established by the method adopted in the article.
Competing interests
None declared