We establish several rank equalities for idempotent and involutory matrices. In particular, we obtain new formulas for the rank of the difference, the sum, the product and the commutator of idempotent or involutory matrices. Extensions to scalar-potent matrices are also included. Our matrices are complex and are not necessarily Hermitian. (C) 2001 Elsevier Science Inc. All rights reserved. [References: 19]
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