When is a matrix a difference of two idempotents

1990/03/01 by Robert E. Hartwig, Mohan S. Putcha · 6 citations
Mathematics · Computer Science · Engineering · #Advanced Topics in Algebra #Matrix Theory and Algorithms #graph theory and CDMA systems

paper · doi:10.1080/03081089008817983

Abstract

Necessary and sufficient conditions are given for a matrix A to be a sum or a difference of two idempotents. These conditions are expressed in terms of (i) the block structure of A under similarity, as well as (ii) the elementary divisor structure of A.

Cited by

• Triangular idempotent matrices over a general ring
• When is a matrix a sum of idempotents?
• Idempotents in triangular matrix rings
• Sums of two triangularizable quadratic matrices over an arbitrary field
• Strongly nil-clean 2-by-2 matrices over general commutative rings
• (k+1)-potent Matrices in triangular matrix Groups and Incidence Algebras of Finite Posets

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