Idempotency of linear combinations of an idempotent matrix and a tripotent matrix
Let \(A\) be a matrix with entries in the complex numbers. Then \(A\) is called idempotent if \(A^2=A\), it is called tripotent if \(A^3=A.\) If \(B_1\) and \(B_2\) are nonzero idempotent matrices, then \(B=B_1-B_2\) is called essentially tripotent. Suppose \(A\) is idempotent, \(B\) is essentially tripotent, and \(c_1,c_2\neq 0.\) The authors determine when a linear combination \(c_1A+c_2B\) is idempotent.
scientific article; zbMATH DE number 1864711