Generalized and hypergeneralized projectors. (English) Zbl 0887.15024
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.
Reviewer: H.Havlicek (Wien)
MSC:
| 15B57 | Hermitian, skew-Hermitian, and related matrices |
| 15A09 | Theory of matrix inversion and generalized inverses |
Keywords:
quadripotent matrix; range; tripotent matrix; generalized projector; hypergeneralized projectorReferences:
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