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When is a matrix a sum of idempotents? (English) Zbl 0696.15011
Let M be an \(n\times n\) matrix with elements in an algebraically closed field. The authors prove that M is a sum of idempotents if and only if \(tr(M)=ke\) where k is an integer with \(k\geq rank M\). They also prove that if A is an \(n\times n\) matrix of integers then A is a sum of integral idempotents if rank A\(<tr(A)\), and is not a sum of integral idempotents if rank A\(>tr(A)\). If rank A\(=tr(A)\), A may or may not be a sum of integral idempotents.
Reviewer: F.J.Gaines

MSC:
15A21 Canonical forms, reductions, classification
15B36 Matrices of integers
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[1] DOI: 10.1017/S0017089500000173 · Zbl 0157.07101
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