Absolutely Flat Idempotents

Abstract

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A real $n$-by-$n$ idempotent matrix $A$ with all entries having the same absolute value is called {\it absolutely flat}. We consider the possible ranks of such matrices and herein characterize the triples: size, constant, and rank for which such a matrix exists. Possible inequivalent examples of such matrices are also discussed.
11 pages, Electronic Journal of Linear Algebra

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