Sums of idempotent matrices. (English) Zbl 0724.15012
Author’s summary: We show that any complex square matrix T is a sum of finitely many idempotent matrices if and only if tr T is an integer and tr \(T\geq rank T\). Moreover, in this case the idempotents may be chosen such that each has rank one and has range contained in that of T. We also consider the problem of the minimum number of idempotents needed to sum to T and obtain some partial results.
Reviewer: T.Nôno (Hiroshima)
MSC:
| 15A21 | Canonical forms, reductions, classification |
References:
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