Singular matrices as products of idempotents.

After a short history of this problem we will first give some examples of matrices that are always product of idempotent matrices. We will then present the case of matrices over a division rings, local rings, quasi-euclidean rings. In the second part of the talk we will consider the case of singular nonnegative matrices (over the real numbers) and examine when they are product of nonnegative idempotent matrices. We will end this talk mentioning nice results obtained by Hannah and O'Meara about decomposing elements of a regular rings into idempotent.

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Date and Venue

Start Date
Venue
Room FC1 004, Mathematics building, FCUP

Speaker

André Leroy

Speaker's Institution

Université d'Artois

Area

Algebra, Combinatorics and Number Theory