On the Open Problem Related to Rank Equalities for the Sum of Finitely Many Idempotent Matrices and Its Applications
نویسندگان
چکیده
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.
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ورودعنوان ژورنال:
دوره 2014 شماره
صفحات -
تاریخ انتشار 2014