Generalized and hypergeneralized projectors
A complex \(n\times n\) matrix \(A\) satisfying \(A=A^3\), \(A=A^4\), \(A^2=A^*\) (conjugate transpose) or \(A^2=A^+\) (Moore-Penrose inverse) is called tripotent, quadripotent, generalized projector or hypergeneralized projector, respectively. The authors give a series of characterizations, e.g. for normal quadripotent and quadripotent matrices \(A\) satisfying range \(A=\) range \(A^*\). Conditions for the sum, difference and product of (hyper-)generalized projectors to be a mapping of the same kind are given.
scientific article; zbMATH DE number 1076307
scientific article