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MATHEMATICA BOHEMICA, Vol. 126, No. 1, pp. 237-246 (2001)
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# Block diagonalization

## J. J. Koliha

* J. J. Koliha*, Department of Mathematics and Statistics, The University of Melbourne, VIC 3010, Australia, e-mail: ` j.koliha@ms.unimelb.edu.au`

**Abstract:**
We study block diagonalization of matrices induced by resolutions of the unit matrix into the sum of idempotent matrices. We show that the block diagonal matrices have disjoint spectra if and only if each idempotent matrix in the inducing resolution double commutes with the given matrix. Applications include a new characterization of an eigenprojection and of the Drazin inverse of a given matrix.

**Keywords:** eigenprojection, resolutions of the unit matrix, block diagonalization

**Classification (MSC2000):** 15A21, 15A27, 15A18, 15A09

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