Nonsingularity of linear combinations of idempotent matrices
The authors show that, for idempotent \(n\times n\) complex matrices \(P_1\) and \(P_2\), the nonsingularity of \(P_1+P_2\) is equivalent to the nonsingularity of \(c_1P_1+c_2P_2\), where \(c_1\) and \(c_2\) are nonzero complex numbers satisfying \(c_1+c_2\neq0\).
scientific article; zbMATH DE number 2105728