title: On the open problem related to rank equalities for the sum of finitely many idempotent matrices and its applications.
abstract: Tian and Styan have shown many rank equalities for the sum of two and three idempotent matrices and pointed out that rank equalities for the sum P₁ + ⋯+P k with P₁,…, P k be idempotent (k > 3) are still open. In this paper, by using block Gaussian elimination, we obtained rank equalities for the sum of finitely many idempotent matrices and then solved the open problem mentioned above. Extensions to scalar-potent matrices and some related matrices are also included.
authors.affiliation: School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, Fujian 350007, China ; School of Mathematics, Putian University, Putian, Fujian 351100, China.
authors.forename: Mei-xiang
authors.initials: MX
authors.lastname: Chen
authors.affiliation: School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, Fujian 350007, China.
authors.forename: Qing-hua
authors.initials: QH
authors.lastname: Chen
authors.affiliation: Institute of Applied Physics and Computational Mathematics, Beijing 100094, China.
authors.forename: Qiao-xin
authors.initials: QX
authors.lastname: Li
authors.affiliation: School of Mathematics, Putian University, Putian, Fujian 351100, China.
authors.forename: Zhong-peng
authors.initials: ZP
authors.lastname: Yang
mesh_terms: D055641:Mathematical Concepts; D009716:Numerical Analysis, Computer-Assisted