The spectrum of matrices depending on two idempotents
The spectrum of the sum of idempotent matrices is studied. To be more precise, let \(P=P^2\) and \(Q=Q^2\) be idempotent matrices and \(a,b \in C\). Then the spectrum of \(aP+bQ\) can be related to the spectrum of \(P-Q, PQ, PQP\) and \(PQ-QP\). Here it is assumed that \(aP+bQ\) is diagonalizable. The results lead to simpler proofs of several results in the literature.
scientific article; zbMATH DE number 5919232
scientific article